Question

if you know one answer
please give one answer if you know both then I will give you brainlist answer​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{( \frac{a}{2b} + \frac{2b}{a} )^{2} - ( \frac{a}{2b} - \frac{2b}{a} )^{2} - 4 =0}}}$

$\green{\tt{\therefore{(4a + 3b)^{2} - (4a - 3b)^{2} + 48ab = 96ab}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies ( \frac{a}{2b} + \frac{2b}{a} )^{2} - ( \frac{a}{2b} - \frac{2b}{a} )^{2} - 4 \\ \\ \tt: \implies (4a + 3b)^{2} - (4a - 3b)^{2} + 48ab \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies ( \frac{a}{2b} + \frac{2b}{a} )^{2} - ( \frac{a}{2b} - \frac{2b}{a} )^{2} - 4 =? \\ \\ \tt: \implies (4a + 3b)^{2} - (4a - 3b)^{2} + 48ab =?$

• According to given question :

$\bold{As\:we\:know\:that}\\\\ \tt: \implies ( \frac{a}{2b} + \frac{2b}{a} )^{2} - ( \frac{a}{2b} - \frac{2b}{a} )^{2} - 4 \\ \\ \tt: \implies { (\frac{a}{2b}) }^{2} + {( \frac{2b}{a} )}^{2} + 2 \times \frac{a}{2b} \times \frac{2b}{a} - { (\frac{a}{2b}) }^{2} - {( \frac{2b}{a} )}^{2} + 2 \times \frac{a}{2b} \times \frac{2b}{a} - 4\\ \\ \tt:\implies 2+2-4 \\ \\ \tt: \implies 4 - 4 \\ \\ \green{\tt: \implies 0 }\\ \\ \green{\tt \therefore ( \frac{a}{2b} + \frac{2b}{a} )^{2} - ( \frac{a}{2b} - \frac{2b}{a} )^{2} - 4 = 0} \\ \\ \bold{As \: we \: know \: that} \\ \tt : \implies (4a + 3b)^{2} - (4a - 3b)^{2} + 48ab \\ \\ \tt : \implies {(4a)}^{2} + {(3b)}^{2} + 2 \times 4a \times 3b - {(4a)}^{2} - {(3b)}^{2} + 2 \times 4a \times 3b + 48ab\\ \\ \tt : \implies 24ab + 24ab + 48ab \\ \\ \tt : \implies 48ab + 48ab \\ \\ \green{\tt : \implies 96ab} \\ \\ \green{\tt \therefore (4a + 3b)^{2} - (4a - 3b)^{2} + 48ab = 96ab}$

Answer 2

..

$\tt{\huge{\purple{ ..................... }}}$

QueStI0N -

${ ( \dfrac{a}{2b} + \dfrac{2b}{a} ) } ^ 2 - { ( \dfrac{a}{2b} +l- \dfrac{2b}{a} ) } ^ 2 - 4$

${ ( 4a + 3b ) } ^ 2 - { ( 4a - 3b )} ^ 2 + 48ab$

S0LUTI0N -

${ ( \dfrac{a}{2b} + \dfrac{2b}{a} ) } ^ 2 - { ( \dfrac{a}{2b} +l- \dfrac{2b}{a} ) } ^ 2- 4$

$Let \: \dfrac{a}{2b} = p \: and \: \dfrac{2a}{b} = q \\ => { (p+q)}^2 - {(p-q)}^2 = 4pq$ $\\ \\ => Using \: This \: Identity \\ \\ => 4 \times \dfrac{ a}{ 2b } \times \dfrac{2a}{b} - 4\\ \\ => 4- 4 = 0$

${ ( 4a + 3b ) } ^ 2 - { ( 4a - 3b )} ^ 2 + 48ab \\ \\ Let \: 4a = k \: and \: 3b = l \\ \\ Then \::- \\ 4kl + 48ab \\ \\ => 48ab + 48ab \\ \\ => 96ab$