Question

if m and n are the roots of the equation x²-5x+3=0, find the value of (¡) (m+n)²+( m-n)². (¡¡) (m+n)³+4mn​

Answer 1

1. Answer: 38
2. Answer: 137

*Know :

• $m+n=5$ --- 1
• $mn=3$ --- 2

(i) $(m+n)^2+(m-n)^2$

Expand the polynomial.

→ $(m+n)^2+(m-n)^2$

→ $2(m^2+n^2)$

From 1, 2

$m^2+n^2=(m+n)^2-2mn=25-6=19$

This is the answer, $2(m^2+n^2)=38$.

(ii) Evaluate the polynomial.

→ $(m+n)^3+4mn$

→ $5^3+12$

→ $125+12$

→ $137$

This is the answer, 137.