Question

If x-1/x=4,then find the value of x2+1/x2

Answer 1

GIVEN:-

• $\rm{x-\dfrac{1}{x}=4}$

TO FIND:-

• $\rm{x^2+\dfrac{1}{x^2}}$

IDENTITY USED:-

• $\rm{(a-b)^2=a^2-2ab+b^2}$

Now,

$\implies\rm{x-\dfrac{1}{x}=4}$

Squaring the both sides.

$\implies\rm{(x-\dfrac{1}{x})^2=(4)^2}$

$\implies\sf{x^2+\dfrac{1}{x^2}-2\times{\cancel{x}}}\times{\dfrac{1}{\cancel{x}}}=16}$

$\implies\rm{x^2+\dfrac{1}{x^2}-2=16}$

$\implies\rm{x^2+\dfrac{1}{x^2}=18}$.

Hence, The value of $\rm{x^2+\dfrac{1}{x^2}}$ is 18.

SOME MORE IDENTITY.

• $\rm{(a+b)^2=a^2+2ab+b^2}$

• $\rm{a^3+b^3=(a+b)(a^2-ab+b^2)}$

• $\rm{a^3-b^3=(a-b)(a^2+ab+b^2)}$

Answer 2

Answer:

1/-2

Step-by-step explanation:

x-1/x= 4 (given)

(find) x2+1/x2

x-1=4x

4x-x=-1

3x=-1

x=-1/3

(-1/3)2+1/(-1/3)2

(-2/3)+1/(-2/3)

(-2+3)/3/-2/3

1/3/-2/3

1/-2 answer