If x=√(√2+1)/√(√2-1) then the value of x²-1 is?
Answers
Answer:
d 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
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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
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Carl Bryan
Answered 2 years ago
15/4 or -15/4
Bikash Ghondeyy Gurung
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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
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