Question

please help me

if a+b=5, a-b=1 , find the value of 8ab (A2+b2​

Answer 1

Given,

• $\sf{a\:+\:b\:=\:5}$$---(1)$
• $\sf{a\:-\:b\:=\:1}$$---(2)$

Solving (1), we get,

$\implies\sf{a\:+\:b\:=\:5}$

$\implies\sf{a\:=\:5\:-\:b}$$---(3)$

Substituting (3) in (2), we get,

$\implies\sf{a\:-\:b\:=\:1}$

$\implies\sf{5\:-\:b\:-\:b\:=\:1}$

$\implies\sf{-\:b\:-\:b\:=\:1\:-\:5}$

$\implies\sf{-2b\:=\:-4}$

$\implies\sf{b\:=\:{\dfrac{-4}{-2}}}$

$\implies\sf{b\:=\:2}$

Substituting 'b' in (1),

$\implies\sf{a\:+\:b\:=\:5}$

$\implies\sf{a\:+\:2\:=\:5}$

$\implies\sf{a\:=\:5\:-\:2}$

$\implies\sf{a\:=\:3}$

Substituting values in the equation, we get,

$\implies\sf{8\:ab\:(a^2\:+\:b^2)}$

$\implies\sf{8\:(3\:\times\:2)\:(3^2\:+\:2^2)}$

$\implies\sf{8\:(6)\:(9\:+\:4)}$

$\implies\sf{8(6)\:(9\:+\:4)}$

$\implies\sf{48\:\times\:11}$

$\implies\sf{528}$

Hence, the value of 8 ab(a² + b²) = 528.