if x=3+2√2 find the value of x^2+1/x
Answers
Answer:
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Step-by-step explanation:
x=3+22–√1x=13+22–√=3−22–√9−8=3−22–√(x2+1x2)=(x+1x)2−2(x2+1x2)=(3+22–√+3−23–√)2−2(x2+1x2)=36−2=34
If x = 4/ (2√3+3√2), then what is the value of x+1/x?
What is the value of x+1/x if x=7-4√3?
If x=3-2√2, then what is the value of (√x) - (1/√x)?
If x= 3+2√2, then what is the value of (x+1/x)?
If x=3+2√2, then what is the value of √x-1/√x?
Given,
x=3+2√2
Inverse equatio,
1/x=1/3+2√2
=>1/x=(3–2√2){(3+2√2)(3–2√2)}
=>1/x=(3–2√2)/{(3)²-(2√2)²}
=>1/x=(3–2√2)/(9–8)
=>1/x=(3–2√2)/1
=>1/x=3–2√2
=>x+1/x=3+2√2+3–2√2
=>x+1/x=6
=>x²+1/x²=(x+1/x)² -2.x.1/x
=>x²+1/x² =(6)²-2
=>x²+1/x²=36–2
=>x²+1/x²=34
Ans.
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x = (3 + 2√2)
1/x = 1/(3 + 2√2) = 1/(3 + 2√2) * (3 - 2√2)/(3 - 2√2) = (3 - 2√2)/(9 - 8) =>
1/x = 3 - 2√2
x^2 + 1/x^2:
x + 1/x = (3 + 2√2) + (3 - 2√2) = 6
(x + 1/x)^2 = 6^2
x^2 + 1/x^2 + 2(x)(1/x) = 36
x^2 + 1/x^2 + 2 = 36
x^2 + 1/x^2 = 34
Here x=3+2√2
Therefore, 1/x=1/3+2√2
Or,1/x=(3–2√2){(3+2√2)(3–2√2)}
Or,1/x=(3–2√2)/{(3)²-(2√2)²}
Or,1/x=(3–2√2)/(9–8)
Or,1/x=(3–2√2)/1
Or,1/x=3–2√2
x+1/x=3+2√2+3–2√2
Or,x+1/x=6
Now, x²+1/x²=(x+1/x)² -2.x.1/x
Or,x²+1/x² =(6)²-2
Or,x²+1/x²=36–2
Or,x²+1/x²=34
If x=3+2√3, then what is the value of √x+1/√x?
If ‘x=3-2√2’, can you find the value of ‘√x+1/√x’?
If x = 3+2√3, then what is the value of 1/x?
If x = √3 + √2, then what is the value of (x²+x+1/x + 1/x²)?
If x= (3-2√2), how do you show that (√x-1/√x) =2?
Given,
x=3+2√2
Inverse equatio,
1/x=1/3+2√2
=>1/x=(3–2√2){(3+2√2)(3–2√2)}
=>1/x=(3–2√2)/{(3)²-(2√2)²}
=>1/x=(3–2√2)/(9–8)
=>1/x=(3–2√2)/1
=>1/x=3–2√2
=>x+1/x=3+2√2+3–2√2
=>x+1/x=6
=>x²+1/x²=(x+1/x)² -2.x.1/x
=>x²+1/x² =(6)²-2
=>x²+1/x²=36–2
=>x²+1/x²=34
Ans
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If x = 3 +2√2, then 1/x = 1/(3+2√2) =(3–2√2), because 3^2 -(2√2)^2 =9–8=1. Hence x^2 +(1/x^2) = [x+(1/x)]^2 -2 = 6^2 -2 =36 -2 = 34.
x=3+ 2×(2^0.5) = ((2^0.5)^2) + (1^2) + 2×1×(2^0.5)
= ((2^0.5) + 1)^2 = A^2, say.
Note (x + (1/x) )^2 = (x^2)+(1/(x^2)) + 2 = V+2 where V is the Answer value.
V= (x+ (1/x) )^2 — 2 = ((A^2)+(1/(A^2))^2 — 2
= (A^4) + (1/(A^4)) — 2 =
((2^0.5)+1)^4) + (1/((2^0.5)+1)^4) — 2×A×(1/A)
= (x-(1/x))^2 = ((x^2)-1)/x)^2 = ((x+1)×(x-1)/x)^2
= ((2×(2+(2^0.5)))×(2×(1+(2^0.5))) )^2 ÷ (((2^0.5)+1)^4)
= 16 × ((2+(2^0.5))^2) ÷ (((2^0.5)+1)^2)
Now rationalize the denominator by multiplying with (((2^0.5)-1)^2) to get Denominator = (2-1)^2=1 and the
Numerator = 16× (((2^0.5)+2)×((2^0.5)-1) )^2
= 16×((2 + (2^0.5) -2) ^2)
= 16×2
If x = 4/ (2√3+3√2), then what is the value of x+1/x?
What is the value of x+1/x if x=7-4√3?
If x=3-2√2, then what is the value of (√x) - (1/√x)?
If x= 3+2√2, then what is the value of (x+1/x)?
If x=3+2√2, then what is the value of √x-1/√x?
If x=3+2√3, then what is the value of √x+1/√x?
If ‘x=3-2√2’, can you find the value of ‘√x+1/√x’?
If x = 3+2√3, then what is the value of 1/x?
If x = √3 + √2, then what is the value of (x²+x+1/x + 1/x²)?
If x= (3-2√2), how do you show that (√x-1/√x) =2?
What is the value of (x2+1/x2)(x4+1/x4)/(x3+1/x3), when x+1/x=3-2√2?
If x=3+2√2 then find whether x+1/x is rational or irrational?
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