Question

solve for x (a+b)^2 x^2 +8(a^2-b^2)x +16(a-b)^2=0​

Answer 1

Answer:

"refer the attachment "

Step-by-step explanation:

hope it's helpful

Answer 2

Answer:

$\sf \: (a+b) {}^{2} x {}^{2} +8(a {}^{2} −b {}^{2} )x+16(a−b) {}^{2} =0$

Method-1:

$\boxed{ \sf (a+b) {}^{2} x {}^{2} +8(a+b)(a−b)x+(4(a−b)) {}^{2} =0}$

$\boxed{ \sf⟹((a+b)x+4(a−b)) {}^{2} =0}$

$\boxed{ \sf{⟹x=−4(a−b)a+b}}$

Method-2:

$\sf \boxed{Δ=(8(a2−b2)) {}^{2} −64(a+b) {}^{2} (a−b) {}^{2} }$

$\boxed{ \sf ⟹Δ=64(a+b)2(a−b) {}^{2} −64(a+b) {}^{2} (a−b) {}^{2} =0}$

$\sf \boxed {{x=−8 \: (a2−b2) {}^{2} (a+b) {}^{2} =−4(a−b)a+b=4(b−a)a+b}}$