Question

if A = x^2+y^2 and b = x^2-b ^2 then a+b = ?​

Answer 1

As we know that

(a+b)
2
=a
2
+b
2
+2ab,(a−b)
2
=a
2
+b
2
−2ab

Given (x
2
+y
2
)(a
2
+b
2
)=(ax+by)
2


x
2
(a
2
+b
2
)+y
2
(a
2
+b
2
)=(ax)
2
+(by)
2
+2(ax)(by)

⟹a
2
x
2
+b
2
x
2
+a
2
y
2
+b
2
y
2
=a
2
x
2
+b
2
y
2
+2abxy

⟹b
2
x
2
+a
2
y
2
=2abxy

⟹(bx)
2
+(ay)
2
−2(bx)(ay)=0

⟹(bx−ay)
2
=0

⟹bx=ay

⟹
a
x
​
=
b
y
​