Question

if a/b=b/c then solve (a²+ b²+2ab)/(b² +c²+2bc)= a/c.

My question was wrong last time now it is correct please show step by step .​

Answer 1

$\huge\underline\bold\red{Answer:}$

Hence Proved

$\huge\underline\bold\red{Proof:}$

$\frac{a}{b} = \frac{b}{c}$

${b}^{2} = ac$

$b = \sqrt{ac}$

$LHS = \frac{ (a²+ b²+2ab) }{(b² +c²+2bc)}$

Applying the value of b² and b

$= \frac{ {a}^{2} + ac + 2a \sqrt{ac} }{ac + {c}^{2} + 2c \sqrt{ac} }$

$= \frac{a(a + c + 2 \sqrt{ac}) }{c(a + c + 2 \sqrt{ac}) }$

$= \frac{a}{c}$

$=RHS$