Question

m+1/m=-5 then prove that m^2+1/m^2=23​

Answer 1

Answer:

23

Step-by-step explanation:

m+1/m=5

squaring both sides

(m+1/m)²=25

m²+1/m²+2=25

m²+1/m²=25-2=23

Answer 2

$m+\dfrac{1}{m} = -5\\\\\text{squaring both sides}\\\\\\\Big(m+\dfrac{1}{m}\Big)^2= (-5)^2\\\\\\m^2+\dfrac{1}{m^2}+\Big(2\times\diagup\!\!\!\!\!{m}\times\dfrac{1}{\diagup\!\!\!\!\!m}\Big)=25\\\\\\m^2+\dfrac{1}{m^2}=25-2\\\\\\\boxed{\bold{m^2+\dfrac{1}{m^2}=23}}$