Question

If a and b are rational number and 2+✓5/2-✓5=a+b✓3 find value of a and b also a^2+b^2

Answer 1

$here \: is \: your \: answer \: \\ = 2 + \sqrt{5} by2 - \sqrt{5} = a + b \sqrt{3} \\ \frac{2 + \sqrt{5} }{2 - \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} } \\ \frac{(2 - \sqrt{5 {}^{2} } }{2 {}^{2} - ( - \sqrt{5} {}^{2} } \: \: \: \: \: \: \: \: (a - b) {}^{2} = {a}^{2} {b}^{2} = - 2ab \\ \frac{(2 - \sqrt{5})(2 - \sqrt{5}) }{4 - 5} \\ \frac{4 - 2 \sqrt{5} + 2 \sqrt{5} + 5 }{1 } \\ \frac{4 - 5}{1 } \\ \frac{1}{1 \\ } ans$ and then insert the value a+b root 3

then the answer will come a-7 b-4

Answer 2

first we multiply the numerator & denominator by (3√2+2√3) then we use formula in the denominator = a+b)(a-b) = a^2-b&2

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The value of a= 2 & b= -5/6

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