Question

Solve the question with algebraic identity​

Answer 1

Step-by-step explanation:

Given - x^{2} + \frac{1}{ x^{2} } = 66x

2

+

x

2

1

=66

We have the identity,

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

2

+

x

2

1

=(x−

x

1

)

2

+2

(Derived from the original identity,

(a - b)^{2} = a^{2} + b^{2} - 2ab(a−b)

2

=a

2

+b

2

−2ab )

By putting values,

(x - \frac{1}{x})^{2} + 2(x−

x

1

)

2

+2 = 66

(x- \frac{1}{x}) ^{2}(x−

x

1

)

2

= 66 - 2

(x- \frac{1}{x}) ^{2}(x−

x

1

)

2

= 64

x - \frac{1}{x}x−

x

1

= \sqrt{64}

64

x - \frac{1}{x}x−

x

1

= +/- 8

=8

Hope it helped!