Question

Answer 1

⇒a−b−1=b−c−1=a−c2⇒−2(a−b)=−2(b−c)=c−a⇒M=4(a−b)(b−c)−(c−a)2=4(a−b)2−(c−a)2=[−2(a−b)]2−(c−a)2=(c−a)2−(c−a)2=0

Answer 2

\(b^2=ac\Rightarrow\dfrac{a}{b}=\dfrac{b}{c};c^2=bd\Rightarrow\dfrac{b}{c}=\dfrac{c}{d}\Rightarrow\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\\ \Rightarrow\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}=\dfrac{2a+3b-4c}{2b+3c-4d}\\ \Rightarrow\dfrac{a^3}{b^3}=\dfrac{b^3}{c^3}=\dfrac{c^3}{d^3}=\dfrac{a^3+b^3-c^3}{b^3+c^3-d^3}=\left(\dfrac{2a+3b-4c}{2b+3c-4d}\right)^3\)