Question 63
If $$5^{\sqrt[3]{x}} + 12^{\sqrt[3]{x}} = 13^{\sqrt[3]{x}}$$, then the value of $$x$$ is:
Solution
The numbers 5, 12 and 13 form a pythagorean triplet as $$5^2 + 12^2 = 13^2 $$
So comparing $$5^{\sqrt[3]{x}} + 12^{\sqrt[3]{x}} = 13^{\sqrt[3]{x}}$$ with above written pythagorean formula
We get, $$ \sqrt[3]{x} = 2$$
$$\therefore x=2^3 = 8$$
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