(√2+1 )² – ( √2–1 )²( don't give unnecessary answers ) ( give correct answer onl...

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:\dfrac{8(5 \sqrt{2} + 1)}{ {( \sqrt{2} + 1)}^{2} - {( \sqrt{2} - 1) }^{2} }$

$\rm \: = \: \: \:\dfrac{8(5 \sqrt{2} + 1)}{ 4 \times \sqrt{2} \times 1}$

$\: \: \: \: \: \: \: \bigg( \because \: {(x + y)}^{2} - {(x - y)}^{2} = 4xy\bigg)$

$\rm \: = \: \: \:\dfrac{ \cancel4 \times 2 \times (5 \sqrt{2} + 1)}{ \cancel4 \times \sqrt{2} }$

$\rm \: = \: \: \:\dfrac{ 2 \times (5 \sqrt{2} + 1)}{ \sqrt{2}}$

$\rm \: = \: \: \:\dfrac{ \cancel{\sqrt{2}} \times \sqrt{2} \times (5 \sqrt{2} + 1)}{ \cancel{\sqrt{2}}}$

$\rm \: = \: \: \: \sqrt{2} \times (5 \sqrt{2} + 1)$

$\rm \: = \: \: \:10 + \sqrt{2}$

Hence,

$\bf :\longmapsto\:\dfrac{8(5 \sqrt{2} + 1)}{ {( \sqrt{2} + 1)}^{2} - {( \sqrt{2} - 1) }^{2} } = 10 + \sqrt{2}$