Question

If x-(1/x) = 3 . Then find using identity x^2- (1/x^2)

Answer 1

Question should be:

• If x-(1/x) = 3 . Then find using identity x²+ (1/x²)

ANSWER:

• Value of the above expression is 11.

GIVEN:

$x - \dfrac{1}{x} = 3$

TO FIND:

$x {}^{2} + \dfrac{1}{x {}^{2} }$

SOLUTION:

$\implies \: x - \dfrac{1}{x} = 3 \\ \\ \: \: \: \: squaring \: both \: sides \\ \implies \: (x - \dfrac{1}{x} ) {}^{2} = (3) {}^{2} \\ \\ \implies \: (x) {}^{2} +( \dfrac{1}{x} ) {}^{2} - 2 \times x \times \dfrac{1}{x} = 9 \\ \\ \implies \: x {}^{2} + \dfrac{1}{x {}^{2} } - 2 = 9 \\ \\ \implies \: x {}^{2} + \dfrac{1}{x {}^{2} } = 9 + 2 \\ \\ \implies \: x {}^{2} + \dfrac{1}{x {}^{2} } = 11$

Value of the above expression is 11.

Answer 2

Answer:

x-1/x=3

then,

(x²)-(1/x)²=(x+1/x)(x-1/x) (using the identity a²-b²)

= (x+1/x)*3

= 3x+3/x

and,

(x-1/x)²=(x-1/x)²

(3)² =x²+1/x²-2

9 = x²+1/x²-2

:. x²+1/x²=9+2

= 11.

here is your answer mates!!!