The proof of $\left(\dfrac{a+b}{b+c}\right)^2 = \dfrac{a^2+b^2}{b^2+c^2}$ given $a:b = b:c$ uses the substitution $b^2 =

Question

The proof of $\left(\dfrac{a+b}{b+c}\right)^2 = \dfrac{a^2+b^2}{b^2+c^2}$ given $a:b = b:c$ uses the substitution $b^2 = ac$ and the expansion—

Accepted Answer

$(a+b)^2 = a^2 + 2ab + b^2$

Answer

$(a-b)^2 = a^2 - 2ab + b^2$

Answer

$a^3 + b^3 = (a+b)(a^2-ab+b^2)$

Answer

$a^2 - b^2 = (a-b)(a+b)$

The proof of (a+bb+c)2=a2+b2b2+c2\left(\dfrac{a+b}{b+c}\right)^2 = \dfrac{a^2+b^2}{b^2+c^2}(b+ca+b​)2=b2+c2a2+b2​ given a:b=b:ca:b = b:ca:b=b:c uses the substitution b2=acb^2 = acb2=ac and the expansion—