Question

Find the value of (4x+9)^½ + (4x -9)^½=5+(7)^½

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Answer 1

(4x+9)^½ +(4x-9)^½ = 5+7^½

$\: \sqrt{4x+9} + \sqrt{ 4x-9} = 5+ \sqrt{7} \\ Squaring \: on \: both \: sides \\</p><p> 4x+9 +4x-9 =( 5+ \sqrt{7}) ^{2} \\ 8x = 5^{2} + (\sqrt{7} ) ^{2} + 2(5) (\sqrt{7} ) \\ 8x = 25 + 7 + 10 \sqrt{7} \\ 8x = 32 + 10 \sqrt{7} \\ x = \frac{32 + 10 \sqrt{7} }{8} \\ x = \frac{16 + 5 \sqrt{7} }{4}$