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dsp73
1 year ago
15

Calculate a and b if

Mathematics
1 answer:
const2013 [10]1 year ago
4 0

Notice that

7^{2014} - 7^{2012} = 7^{2012} \bigg(7^2 - 1\bigg) = 7^{2012} \times 48 = 2^4 \times 3 \times 7^{2012}

12=2^2\times3, so

\dfrac{7^{2014}-7^{2012}}{12} = 2^2 \times 7^{2012}

Then taking the positive square root gives

\sqrt{\dfrac{7^{2014}-7^{2012}}{12}} = \sqrt{2^2 \times 7^{2012}} = 2\times7^{1006}

so \boxed{a=2} and \boxed{b=1006}.

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