Surds and Indices Practice Test 2

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Question : 14 of 17

Marks: +1, -0

Given that

a^x = b^y = c^z

and

b^2 = ac

, then find the value of y

${2xz}/{x+z}$
${xz}/{2(z-x)}$
${xz}/{2(x-z)}$
${xz}/{x+2}$

Solution:

Let

a^x = b^y = c^z=k,

then

a = k^{1/x} ; b = k^{1/y} ; c = k^{1/z}

Now,

b^2=ac

⇒(k^{1/y})^2=k^{1/x}×k^{1/z}

⇒ k^{2/y} =k^{1/x+1/z}

⇒2/y=1/x+1/z

⇒y={2xz}/{x+z}

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