if x=√2-1, then find the value
of x²+1/x²
Give me full explanation of this question
and full answer
Answers
Answer:
Given ,
x-(1/x) = 3/2 ———(1)
Now,
[x+(1/x)]^2 = [x-(1/x)]^2 + 4x * (1/x) = (3/2)^2 + 4 = 9/4 + 4 = (16+9)/4 = 25/4
x+(1/x) = √(25/4) = 5/2 ——-(2)
x^2 - (1/x)^2
= [x+(1/x)] * [x-(1/x)]
Put (1) & (2),
= 5/2 * 3/2
= 15/4 (ans)
Neeta Singh
Answered 3 years ago
(x-1/x)²=(x+1/x)²-4
9/4+4=(x+1/x)²
25/4=(x+1/x)²
X+1/x=±5/2
x²-1/x²=(x-1/x)(x+1/x)
x²-1/x²=(3/2)(±5/2)=±15/4
Get a life cover with Canara HSBC OBC iSelect term plan.
Carl Bryan
Answered 2 years ago
15/4 or -15/4
Bikash Ghondeyy Gurung
If (x+1/x)=2, what is the value of (x-1/x)?
1,152 Views
If (x + 1/x) = 4 and (x^2 + 1/x^3) = 12, then what is the value of (x^3 + 1/x^2)?
12,276 Views
If (x +1/x) = 9 and (x^2 + 1/x^2) = 53 then find the value of (x - 1/x)?
16,384 Views
If x^2+1/x^2 =23, what is the value of 'x'?
21,576 Views
What is the LCM of x and 1/x?
2,319 Views
Kimtee Goh
Answered 4 years ago
⑴ x-1/x=3/2
2x² -3x-2=0
(2x+1(x-2))
x=2 or x=-½
⑵ ∴f(x)=x²-(1/x²)↙
(i)) when =2 ，
f(x)=2²—1/(2²)
=4-¼=3¾ ↙
⑶ when x= -½
f(x)=(-½)²—1/(-½)²=¼—1/¼=¼-4=-3¾ ↙
∴ x≈² —(1/x²)=±3¾
Krishna B Pandit
Answered 3 years ago
x²-1/x²=(x+1/x)(x-1/x).
x+1/x=√(x-1/x)²+4 = √((3/2)²+4).
x+1/x= 5/2. Hence x²-1/x² = 3/2*5/2=15/4.
Kanchan Bala
Mike Hirschhorn
Answered 7 months ago
x-1/x=3/2.
Square this, add 4, take the square root.
x+1/x=+-5/2.
average the two.
x=2 or -1/2
x^2–1/x^2 = 15/4 or -15/4.
Save taxes & secure your family's future, with a term plan.
Trí Lại Thành
Answered 4 years ago
make the square both side of second equation we will get value of x^2+1/x^2 and from that we can get value of (x+1/x)^2 and after that we can know for sure the value of x^2-1/x^2 =(x+1/x)(x-1/x) and ...
Jay Gousai
Answered 4 years ago
15/4
Abid Ali
Answered 1 year ago
17/4
What is x2+1x2, given x+1x=1?
320,720 Views
If x² + 1/x² =38 then what is the value of (x- 1/x)?
2,285 Views
What is the value of x²-(1/x²) when 5x-(1/x) =3/2?
598 Views
If x+1/x=3, then what is the value of x³+1/x³=?
117,932 Views
If x+(1/x)=2, then what is the value of x-(1/x) =?
22,527 Views
If (x+1/x)=2, what is the value of (x-1/x)?
1,152 Views
If (x + 1/x) = 4 and (x^2 + 1/x^3) = 12, then what is the value of (x^3 + 1/x^2)?
12,276 Views
If (x +1/x) = 9 and (x^2 + 1/x^2) = 53 then find the value of (x - 1/x)?
16,384 Views
If x^2+1/x^2 =23, what is the value of 'x'?
21,576 Views
What is the LCM of x and 1/x?
2,319 Views
If x+1/x=9 what is the value of x-1/x=?
84,730 Views
If x+1/x = 4, then what is x^4+1/x^4?
1,989 Views
How would you solve x(x+1)(x+2)(x+3)=x(x+1)(x+2)(x+3)(x+4)?
44,799 Views
If x-x÷2=5÷2, what will be the value of x?
603 Views
What is the value of x²+1/x², if x- 1/x =✓3?
1,538 Views
Find x2−1x2 when
x−1x=32
If it was a plus sign in the squared sum we could do this without solving just by squaring the form we know to be 3/2. But with the minus we might as well solve:
2x2−3x−2=0
(2x+1)(x−2)=0
x=−12 or x=2
x2−1x2=14−4=−114 or x2−1x2=4−14=114
Putting it together, we can’t tell the sign of the difference:
x2−1x2=±154
Check: 2−1/2=3/2.✓4–1/4=15/4✓
−1/2−(1/(−1/2))=3/2.✓1/4−4=−15/4✓
The fact that it came out with ± gives me a hint how to do it without solving:
(x−1x)2=(32)2
x2+1x2−2=9/4
(x2+1x2)2=(17/4)2
x4+1x4=172/16−2
s=x2−1x2
s2=x4+1x4−2=172/16−4=225/16
s=±154
What is x2+1x2 , given x+1x=1 ?
320,720 Views
If x² + 1/x² =38 then what is the value of (x- 1/x)?
2,285 Views
What is the value of x²-(1/x²) when 5x-(1/x) =3/2?
598 Views
If x+1/x=3, then what is the value of x³+1/x³=?
117,932 Views
If x+(1/x)=2, then what is the value of x-(1/x) =?
22,527 Views
Rashmita Pradhan
Answered 4 years ago
Given ,
x-(1/x) = 3/2 ———(1)
Now,
[x+(1/x)]^2 = [x-(1/x)]^2 + 4x * (1/x) = (3/2)^2 + 4 = 9/4 + 4 = (16+9)/4 = 25/4
x+(1/x) = √(25/4) = 5/2 ——-(2)
x^2 - (1/x)^2
= [x+(1/x)] * [x-(1/x)]
Put (1) & (2),
= 5/2 * 3/2
= 15/4 (ans)
Neeta Singh
Answered 3 years ago
(x-1/x)²=(x+1/x)²-4
9/4+4=(x+1/x)²
25/4=(x+1/x)²
X+1/x=±5/2
x²-1/x²=(x-1/x)(x+1/x)
x²-1/x²=(3/2)(±5/2)=±15/4
Save taxes & secure your family's future, with a term plan.
Carl Bryan
Answered 2 years ago
15/4 or -15/4
Bikash Ghondeyy Gurung
If (x+1/x)=2, what is the value of (x-1/x)?
1,152 Views
If (x + 1/x) = 4 and (x^2 + 1/x^3) = 12, then what is the value of (x^3 + 1/x^2)?
12,276 Views
If (x +1/x) = 9 and (x^2 + 1/x^2) = 53 then find the value of (x - 1/x)?
16,384 Views
If x^2+1/x^2 =23, what is the value of 'x'?
21,576 Views
What is the LCM of x and 1/x?
2,319 Views
Kimtee Goh
Answered 4 years ago
⑴ x-1/x=3/2
2x² -3x-2=0
(2x+1(x-2))
x=2 or x=-½
⑵ ∴f(x)=x²-(1/x²)↙
(i)) when =2 ，
f(x)=2²—1/(2²)
=4-¼=3¾ ↙
⑶ when x= -½
f(x)=(-½)²—1/(-½)²=¼—1/¼=¼-4=-3¾ ↙
∴ x≈² —(1/x²)=±3¾
Krishna B Pandit
Answered 3 years ago
x²-1/x²=(x+1/x)(x-1/x).
x+1/x=√(x-1/x)²+4 = √((3/2)²+4).
x+1/x= 5/2. Hence x²-1/x² = 3/2*5/2=15/4.
Kanchan Bala
Mike Hirschhorn
Answered 7 months ago
x-1/x=3/2.
Square this, add 4, take the square root.
x+1/x=+-5/2.
average the two.
x=2 or -1/2
x^2–1/x^2 = 15/4 or -15/4.
What is the difference between rote learning vs meaningful learning?
BYJU'S
Answered December 29
Great question! There is a world of difference between Rote Learning and Meaningful Learning. To begin with Rote Learning involves learners repeating statements or pieces of information till they’ve memorised it. Remember the time when you had to learn the Pythagorean theorem of A2+ B2 = C2 ? How many times did you have to repeat it to yourself before you could remember it? Clearly Rote Learning is no fun way of learning. Then why do so many learners still follow the technique? It is because learners are unable to connect new information to what they already know in a logical manner. Simply put, when a learner does not understand a certain concept well enough, he/she relies on trying to memorise it without actually knowing what it means. While such a technique might help students recall answ
Trí Lại Thành
Answered 4 years ago
make the square both side of second equation we will get value of x^2+1/x^2 and from that we can get value of (x+1/x)^2 and after that we can know for sure the value of x^2-1/x^2 =(x+1/x)(x-1/x) and ...
Jay Gousai
Answered 4 years ago
15/4
Abid Ali
Answered 1 year ago
17/4
What is x2+1x2 , given x+1x=1 ?
320,720 Views
If x² + 1/x² =38 then what is the value of (x- 1/x)?
2,285 Views
What is the value of x²-(1/x²) when 5x-(1/x) =3/2?
598 Views
If x+1/x=3, then what is the value of x³+1/x³=?
117,932 Views
If x+(1/x)=2, then what is the value of x-(1/x) =?
22,527 Views
If (x+1/x)=2, what is the value of (x-1/x)?
1,152 Views
If (x + 1/x) = 4 and (x^2 + 1/x^3) = 12, then what is the value of (x^3 + 1/x^2)?
12,276 Views
If (x +1/x) = 9 and (x^2 + 1/x^2) = 53 then find the value of (x - 1/x)?
16,384 Views
If x^2+1/x^2 =23, what is the value of 'x'?
21,576 Views
What is the LCM of x and 1/x?
2,319 Views
If x+1/x=9 what is the value of x-1/x=?
84,730 Views
If x+1/x = 4, then what is x^4+1/x^4?
1,989 Views
How would you solve x(x+1)(x+2)(x+3)= x(x+1)(x+2)(x+3)(x+4) ?
44,799 Views
If x-x÷2=5÷2, what will be the value of x?
603 Views
What is the value of x²+1/x², if x- 1/x =✓3?
1,538 Views
AboutCareersPrivacyTermsContactLanguagesYour Ad Choices