Question

If a = 1/3-√8 and b = 1/3+√8. Find the value of a^2​

Answer 1

Answer:

(1/3-√8)2=1/9-8=1-72/8=-71/8

Answer 2

$Given \: a = \frac{1}{(3-\sqrt{8})} \: and \\b= \frac{1}{(3+\sqrt{8})}$

$i) a = \frac{1\times ( 3+ \sqrt{8})}{(3-\sqrt{8})(3+\sqrt{8})} \\= \frac{3+\sqrt{8}}{3^{2} - (\sqrt{8})^{2} }\\= \frac{3+\sqrt{8}}{9 - 8 }\\= 3 + \sqrt{8} \: --(1)$

$\red{ Value \: of \: a^{2} } \\= ( 3 + \sqrt{8})^{2} \\= 3^{2} + (\sqrt{8})^{2} + 2 \times 3 \times \sqrt{8} \\= 9 + 8 + 6\sqrt{8} \\= 17 + 6 \times 2\sqrt{2} \\= 17 + 12\sqrt{2}$

Therefore.,

$\red{ Value \: of \: a^{2} }\green { = 17 + 12\sqrt{2}}$

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