If `ax+by+c=0 " and " a'x+b'y+c'=0`, then prove that
`x/(bc'-b'c)=y/(ca'-c'a)=1/(ab'-a'b)`

If a + b + c = 0 , then prove that (a+b)^2/(ab) + (b+c)^2/(bc) + (c+a)^2/(ca)=3

The two lines ax+by+c=0 and a'x+b'y+c'=0 are perpendicular if (i) ab'=a'b (ii) ab+a'b'=0 (iii) ab'+a'b=0 (iv) a a'+b b'=0

Prove that x^((b-c)/(bc)) x^((c-a)/(ca)) x^((a-b)/(ab))=1

If ab+bc+ca=0, then solve a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0

Prove that a/(bc(a-b)(a-c))+b/(ca(b-c)(b-a))+c/(ab(c-a)(c-a))=1/(abc)

Without expanding at any state, prove that |(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b))|=0

If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b) , then prove that x^(b^2+bc+c^2).y^(c^2+ca+a^2).z^(a^2+ab+b^2)=1

If ab + bc + ca = 0 , then the value of 1/(a^2 - bc) + 1/(b^2 - ca) + 1/(c^2 - ab) will be :

Prove that |(1/a^(2),bc,b+c),(1/b^(2),ca,c+a),(1/c^(2), ab, a+b)|=0