Question

How to solve this please explain.

Answer 1

Algebra,

We have,

$\sqrt[3]{13x + 37} - \sqrt[3]{13x - 37} = \sqrt[3]{2}$
Let, 13 x + 37 = a and 13x - 37 = b
Now, a - b = 74

Moving to the actual answer
$\sqrt[3]{a} - \sqrt[3]{b} = \sqrt[3]{2} \\ now \: cubing \: the \: both \: sides \: we \: get \\ a - b - {3(ab )}^{ \frac{1}{3} } ( \sqrt[3]{a} - \sqrt[3]{b} ) = 2 \\ 74 - 3 {ab}^{ \frac{1}{3} } \times \sqrt[3]{2} = 2 \\ 3 {ab}^{ \frac{1}{3} } \times {2}^{ \frac{1}{3} } = 72 \\ {(2ab)}^{ \frac{1}{3} } = 24 \\cubing \: the \: both \: sides \ \\ 2ab = 24 \times 24 \times 24 \\ ab = 24 \times 24 \times 12 \\ 13 {x}^{2} - {37}^{2} = 24 \times 24 \times 12 \\ 169 {x}^{2} - 1369 = 6912 \\ 169 {x}^{2} = 8281 \\ {x}^{2} = 49 \\ x = + 7 \: and \: - 7$

That was quite tough one

That's it
Hope it helped (●´ϖ`●)