Question

plzz ans.....Thnk u ....Fifth part plzz ans

Answer 1

HELLO DEAR,

given that:-

a,b,c,d are in continuous propotion

$\frac{a}{b} = \frac{b}{c} = \frac{c}{d} ....(1)\\ = > \frac{a}{b} = \frac{b}{c} ....(2)\\ = > \frac{c}{b} = \frac{b}{a} .....(3) \\ \\ = > \frac{b}{c} = \frac{c}{d} \\ = > \frac{d}{c} = \frac{c}{b} ....(3)$

${( { \frac{a - b}{c} } } + { \frac{a - c}{b} }) ^{2} - {( \frac{d - b}{c} } + \frac{d - c}{b} )^{2} \\ = > {( \frac{a}{c} } - \frac{b}{c} + {\frac{a}{b}} - \frac{c}{b} )^{2} - {( \frac{d}{c} - \frac{b}{c} }+ { \frac{d}{b} - \frac{c}{b} })^{2} \\ = > {( \frac{a}{c} - \frac{c}{b} })^{2} - {( \frac{d}{b} - \frac{b}{c} })^{2} .........using(1) \\ = > {( \frac{a}{c} - \frac{d}{c} })^{2} - {( \frac{d}{b} - \frac{a}{b} })^{2}........from(2) \: and (3) \\ = > \frac{1}{ {c}^{2} } {( a- d})^{2} - \frac{1}{ {b}^{2} } {(d - a})^{2} \\ = > \frac{1}{ {c}^{2} } {( a- d})^{2} - \frac{1}{ {b}^{2} } {(a - d})^{2} \\ = > {(a - d)}^{2} ( \frac{1}{ {c}^{2}} - \frac{1}{ {b}^{2} } )$

I HOPE ITS HELP YOU DEAR,
THANKS

☺️☺️☺️☺️☺️