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if-x-3-7-find-1-8x-2-1-




Question Number 139113 by mathdanisur last updated on 22/Apr/21
if, x=3+(√7)  find, (1/( (√(8x^2 −1))))
$${if},\:{x}=\mathrm{3}+\sqrt{\mathrm{7}} \\ $$$${find},\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{8}{x}^{\mathrm{2}} −\mathrm{1}}} \\ $$
Answered by MJS_new last updated on 22/Apr/21
(1/( (√(8x^2 −1))))=(1/( (√(127+48(√7)))))=(√(127−48(√7)))  (a+b(√7))^2 =127−48(√7) ⇒ a=8∧b=−3  ⇒ answer is 8−3(√7)
$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{8}{x}^{\mathrm{2}} −\mathrm{1}}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{127}+\mathrm{48}\sqrt{\mathrm{7}}}}=\sqrt{\mathrm{127}−\mathrm{48}\sqrt{\mathrm{7}}} \\ $$$$\left({a}+{b}\sqrt{\mathrm{7}}\right)^{\mathrm{2}} =\mathrm{127}−\mathrm{48}\sqrt{\mathrm{7}}\:\Rightarrow\:{a}=\mathrm{8}\wedge{b}=−\mathrm{3} \\ $$$$\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\mathrm{8}−\mathrm{3}\sqrt{\mathrm{7}} \\ $$
Commented by mathdanisur last updated on 22/Apr/21
thanks sir
$${thanks}\:{sir} \\ $$

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