Question

If a+1/a = -2, then find the value of a²+1/a²​

Answer 1

Answer:

a²+1/a² = 2

Step-by-step explanation:

a+1/a = -2

=> (a+1/a)² = (-2)²

=> a²+1/a²+2*a*1/a = 4

=> a²+1/a²+2 = 4

=> a²+1/a² = 4-2

=> a²+1/a² = 2

using formula (x-y)² = x²+y²+2*x*y

Answer 2

Answer:

$\displaystyle{{\boxed{\red{\sf\:a^2\:+\:\dfrac{1}{a^2}\:=\:2}}}}$

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:\left(\:a\:+\:\dfrac{1}{a}\:\right)\:=\:-\:2}$

We have to find the value of,

$\displaystyle{\sf\:\left(\:a^2\:+\:\dfrac{1}{a^2}\:\right)}$

Now,

$\displaystyle{\sf\:\left(\:a\:+\:\dfrac{1}{a}\:\right)\:=\:-\:2}$

$\displaystyle{\implies\sf\:\left(\:a\:+\:\dfrac{1}{a}\:\right)^2\:=\:(\:-\:2\:)^2\:\quad\:-\:-\:-\:[\:Squaring\:both\:sides\:]}$

$\displaystyle{\implies\sf\:a^2\:+\:2\:\times\:\cancel{a}\:\times\:\dfrac{1}{\cancel{a}}\:+\:\dfrac{1}{a^2}\:=\:4\:\quad\:-\:-\:-\:[\:\because\:(\:a\:+\:b\:)^2\:=\:a^2\:+\:2ab\:+\:b^2\:]}$

$\displaystyle{\implies\sf\:a^2\:+\:2\:+\:\dfrac{1}{a^2}\:=\:4}$

$\displaystyle{\implies\sf\:a^2\:+\:\dfrac{1}{a^2}\:=\:4\:-\:2}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:a^2\:+\:\dfrac{1}{a^2}\:=\:2}}}}$