Question

if abcd are in proportion prove that root 3asquare+5csquare/ 3bsquare+5dsquare=a/b

Answer 1

Step-by-step explanation:

abcd are in proportion that means

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

$\sqrt{ \frac{3 {a}^{2} + 5 {c}^{2} }{3 {b}^{2} + 5 {d}^{2} } } \\ = \sqrt{ \frac{3 {a}^{2} + 5 {a}^{2} }{3 {b}^{2} + 5 {b}^{2} } } \\ = \sqrt{ \frac{8 {a}^{2} }{8 {b}^{2} } } \\ = \sqrt{ \frac{ {a}^{2} }{ {b}^{2} } } \\ = \frac{a}{b}$

hence proved