Question 54
If $$6^{\sqrt[4]{x}} + 8^{\sqrt[4]{x}} = 10^{\sqrt[4]{x}}$$, then the value of $$x$$ is:
Solution
$$6^{\sqrt[\ 4]{x}}+\ 8^{\sqrt[\ 4]{x}}=10^{\sqrt[\ 4]{x}}$$
It is a pythagoras triplet in the form of $$6^{\ 2}+\ 8^{\ 2}=10^{\ 2}$$
By Comparing , we get
$$=$$> $$\sqrt[\ 4]{x}=\ 2$$
$$\ x=\ 2^4$$
$$\ x=\ 16$$
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