If x = sqrt{a sqrt[3]{b sqrt{a sqrt[3]{b dots | vedclass

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Question

(A) Given the expression $x = \sqrt{a \sqrt[3]{b \sqrt{a \sqrt[3]{b \dots \infty}}}}.$ Squaring both sides,we get $x^2 = a \sqrt[3]{b \sqrt{a \sqrt[3]

Vedclass · Accepted Answer

$\sqrt[5]{a^3 b}$

Vedclass · Answer

(A) Given the expression $x = \sqrt{a \sqrt[3]{b \sqrt{a \sqrt[3]{b \dots \infty}}}}.$ Squaring both sides,we get $x^2 = a \sqrt[3]{b \sqrt{a \sqrt[3]{b \dots \infty}}}.$ Now,cubing both sides of this equation,we get $(x^2)^3 = a^3 \cdot b \sqrt{a \sqrt[3]{b \dots \infty}}.$ This simplifies to $x^6 = a^3 b x.$ Since $x 
eq 0,$ we can divide by $x$ to get $x^5 = a^3 b.$ Therefore,$x = \sqrt[5]{a^3 b}.$

If $x = \sqrt{a \sqrt[3]{b \sqrt{a \sqrt[3]{b \dots \infty}}}},$ then the value of $x$ is:

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