Question

If a = 9+2root6 and b = 57/a

, then what will be the

value of a2 + b2?​

Answer 1

Answer:

hope it helps you brother

Answer 2

$Given \:a = 9 + 2\sqrt{6} \: --(1)$

$and \: b = \frac{57}{a}$

$\implies b = \frac{57}{(9+2\sqrt{6})} \\= \frac{57(9-2\sqrt{6})}{(9+2\sqrt{6})(9-2\sqrt{6})} \\= \frac{57(9-2\sqrt{6})}{9^{2} -(2\sqrt{6})^{2}} \\= \frac{57(9-2\sqrt{6})}{81 - 24} \\= \frac{57(9-2\sqrt{6})}{57} \\= 9 - 2\sqrt{6} \:--(2)$

$i ) a + b = (1) + (2) \\= 9 + 2\sqrt{6} + 9 - 2\sqrt{6}\\= 18 \: --(3)$

$ii )ab = (9 + 2\sqrt{6})(9 - 2\sqrt{6})\\= 9^{2} -(2\sqrt{6})^{2} \\= 81 - 24 \\= 57 \: --(4)$

$Now, \red { Value \:of \: a^{2} + b^{2} } \\= ( a + b )^{2} - 2ab \\= 18^{2} - 2 \times 57 \: [From \:(3) \:and \: (4) ]$

$= 324 - 114\\= 210$

Therefore.,

$\red { Value \:of \: a^{2} + b^{2} } \green {= 210}$

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