Question 62

If $$3^{\sqrt[4]{x}} + 4^{\sqrt[4]{x}} = 5^{\sqrt[4]{x}}$$, then the value of $$x$$ is:

Solution

$$3^{\sqrt[\ 4]{x}}+\ 4^{\sqrt[\ 4]{x}}=5^{\sqrt[\ 4]{x}}$$

It is a pythagoras triplet in the form of $$3^{\ 2}+\ 4^{\ 2}=5^{\ 2}$$

$$=$$> $$\sqrt[\ 4]{x}=\ 2$$

$$\ x=\ 2^4$$

$$\ x=\ 16$$

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