IIT JEE , AIEEE Forum - Mathematics , Algebra

chinmay_kothekar

(a1x+b1)²+(a2x+b2)²+......................(a_nx+b_n)²=0

1) if a1/a2

b1/b2

c1/c2,

2)if a1/a2=b1/b2=c1/c2

then how many real solutions does this equation has?

cvramana

Since each term is a perfect square, each term should be individually zero.

If a₁ / a₂ ¹ b₁ / b₂ then there are 'n' solutions.

X₁ = - b₁ / a₁ ; X₂ = - b₂ / a₂ ; ......... ; X_n = - b_n / a_n ;

If a₁ / a₂ = b₁ / b₂ , then there is only one solution

X = - b₁ / a₁ = - b₂ / a₂ = ............... = - b_n / a_n