Question

Answer this please its very important

Answer 1

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 !!

Answer 2

$Given : x + \frac{1}{x} = \sqrt{7}$

On Squaring both sides, we get

$(x^2 + \frac{1}{x^2}) = ( \sqrt{7})^2$

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

$(x^2 + \frac{1}{x^2} ) = (5)^2$

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!