If ab= bc and a,b,c > 0 then show that, (i) (a + b + c) (b - c) = ab - c2 (ii) (a2 + b2) (b2 + c2 ) = (ab + bc)2 (iii) a2 + b2ab = a + c b

If ab= bc and a,b,c > 0 then show that, (i) (a + b + c) (b - c) =

1.	If ab= bc and a,b,c > 0 then show that, (i) (a + b + c) (b - c) = ab - c2 (ii) (a2 + b2) (b2 + c2 ) = (ab + bc)2 (iii) a2 + b2ab = a + c b
Answer» If $\frac{a}{b} = \frac{b}{c}$ and $a, b, c$ > 0 then show that, (i) (a + b + c) (b $-$ c) = ab $-$ c² (ii) (a²+ b²) (b²+ c²) = (ab + bc)² (iii) $\frac{a^{2} + b^{2}}{a b} = \frac{a + c}{b}$