Question

ax + by =( a)2 +. ( b)2____ 1.
a + b = 2.a.b __________ 2.
solve this equation with any mehtod.
ans. x = a + b
y = a- b

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Answer 1

ANSWER

Taking x+y=u and x−y=v the given system of equations becomes

au+bu−(a2−ab+b2)=0

au−bv−(a2+ab+b2)=0

By cross-multiplication, we have

⇒b×−(a2+ab+b2)−(−b)×−(a2−ab+b2)u=a×−(a2+ab+b2)+a(a2−ab+b2)−v=a×−b−a×b1

⇒−b(a2+ab+b2)−−b(a2−ab+b2)u=−a(a2+ab+b2)+a(a2−ab+b2)−v=−ab−ab1