Question

plz give answer fast​ no spam

Answer 1

$\large\underline\bold{ANSWER \red{\huge{\checkmark}}}$

$\pink{\overbrace{ \underbrace{ \red{\mid\star\mid \:\: \purple{ x= \dfrac{4}{15} \:or\: \dfrac{3}{5}} } \:\: \red{\mid\star\mid}}}}$

EXPLANATION IN DETAILS

$\large\underline\bold{GIVEN,}$

$\leadsto \dfrac{(5x+2)^2 + (5x-2)^2}{(5x+2)^2-(5x-2)^2}= \dfrac{13}{12}$

$\natural \: first\:solving\:the\: equation. \dfrac{(5x+2)^2 + (5x-2)^2}{(5x+2)^2-(5x-2)^2}= \dfrac{13}{12}$

$\large\underline\bold{SOLUTION,}$

$\leadsto \dfrac{(5x+2)^2 + (5x-2)^2}{(5x+2)^2-(5x-2)^2}= \dfrac{13}{12}\\ \\ :\implies 12\times[(5x+2)^2+(5x-2)^2]= 13\times [ (5x+2)^2-(5x-2)^2]\\ \\ :\implies 12[25x^2+4+\:\cancel{20x}+25x^2+4-\:\cancel{20x}=13[\cancel{25x^2+4}+20x-(\cancel{25x^2+4}-20x)] \\ \\ :\implies (50x^2+8)\times 12= 40x\times 13 \\ \\ :\implies 600x^2+96=520x \\ \\ :\implies 600x^2-520x+96=0 \\ \\ :\implies 600x^2-360x-160x+84=0 \\ \\ :\implies 8(75x^2-45x-20x+12)=0 \\ \\ :\implies 8(15x-4)(5x-3)=0 \\ \\ :\implies 15x-4=0 \: or\: 5x-3=0 \\ \\ :\implies x=\dfrac{4}{15}\:\: ,\:\: \dfrac{3}{5} \\ \\ \\ \leadsto \red{ x=\dfrac{4}{15}\:\: ,\:\: \dfrac{3}{5}} \\ \\ \\ \\ \bf{ \boxed{ \blue{ \overline{\underline{ \mid\heartsuit\mid \: x=\dfrac{4}{15}\:\: ,\:\: \dfrac{3}{5}\: \mid\heartsuit \mid }}}}}$