Question

m²+n²+2m= -1 , then find the value of m¹⁹²+n¹⁹⁵​

Answer 1

Step-by-step explanation:

We have,

$\tt{{m}^{2} + n^{2} + 2m = - 1 }$

$\sf{ \implies{m}^{2} + n^{2} + 2m + 1 = 0 }$

$\sf{ \implies{m}^{2} + 2m + 1 + {n}^{2} = 0 }$

$\sf{ \implies{(m + 1)}^{2} + {n}^{2} = 0 }$

Now, we have, sum of two positive quantities is ZERO.

This is possible if each term =0 so,

$\sf{ \implies \: m + 1 = 0 \: \: and \: \: n = 0}$

$\sf{ \implies \: m = - 1 \: \: and \: \: n = 0}$

Now,

$\sf{ {m}^{192} + {n}^{195} }$

$\sf{ = {( - 1)}^{192} + {(0)}^{195} }$

$\sf{ = 1 }$