Answer this please its very important
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Answer is 23,
Solution :
(1) Formulas required : (i) [a+b]² = a² + 2ab + b²,
Given that,
x + (1/x) = √7,
Now, Squaring on both sides,
=> (x + (1/x))² = √7²,
=> x² + 2(x)(1/x) + (1/x)² = 7
=> x² + (1/x²) + 2 = 7,
=> x² + (1/x²) = 5,
Again, Squaring on both sides,
=> (x² + (1/x²))² = 5²
=> x⁴ + 2(x²)(1/x²) + (1/x⁴) = 25,
=> x⁴ + (1/x⁴) + 2 = 25,
=> x⁴ + (1/x⁴) = 23,
Therefore : The value of x⁴ + 1/x⁴ = 23,
Hope you understand, Have a Great day !
Thanking you, Bunti 360 !!
Solution :
(1) Formulas required : (i) [a+b]² = a² + 2ab + b²,
Given that,
x + (1/x) = √7,
Now, Squaring on both sides,
=> (x + (1/x))² = √7²,
=> x² + 2(x)(1/x) + (1/x)² = 7
=> x² + (1/x²) + 2 = 7,
=> x² + (1/x²) = 5,
Again, Squaring on both sides,
=> (x² + (1/x²))² = 5²
=> x⁴ + 2(x²)(1/x²) + (1/x⁴) = 25,
=> x⁴ + (1/x⁴) + 2 = 25,
=> x⁴ + (1/x⁴) = 23,
Therefore : The value of x⁴ + 1/x⁴ = 23,
Hope you understand, Have a Great day !
Thanking you, Bunti 360 !!
Answered by
2
On Squaring both sides, we get
x^2 + 1/x^2 + 2 * x * 1/x = 7
x^2 + 1/x^2 + 2 = 7
x^2 + 1/x^2 = 7 - 2
x^2 + 1/x^2 = 5.
On Squaring both sides, we get
x^4 + 1/x^4 + 2 * x^2 * 1/x^2 = 25
x^4 + 1/x^4 + 2 = 25
x^4 + 1/x^4 = 25 - 2
x^4 + 1/x^4 = 23.
Hope this helps!
siddhartharao77:
Gud Luck.
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