Question

Вычислить : 3/7(4-√2)(3/(1-√2)+ (2/(2 +√2) +3/(3-2√2))

Answer 1

$frac{3(4 - sqrt{2} )}{7} ( frac{3}{1 - sqrt{2} } + frac{2}{2 + sqrt{2} } + frac{3}{3 - 2 sqrt{2} } ) = frac{3(4 - sqrt{2}) }{7} ( frac{3(1 + sqrt{2} )}{(1 - sqrt{2} )(1 + sqrt{2}) } + frac{2(2 - sqrt{2} )}{(2 + sqrt{2} )(2 - sqrt{2} )} + frac{3(3 + 2 sqrt{2}) }{(3 - 2 sqrt{2} )(3 + 2 sqrt{2}) } ) = frac{3(4 - sqrt{2} )}{7} ( frac{3(1 + sqrt{2}) }{1 - 2} + frac{2(2 - sqrt{2} )}{4 - 2} + frac{3(3 + 2 sqrt{2}) }{9 - 8} = frac{3(4 - sqrt{2} )}{7} ( - 3 - 3 sqrt{2} + 2 - sqrt{2} + 9 + 6 sqrt{2} ) = frac{3(4 - sqrt{2}) }{7} (2 sqrt{2} + 8) = frac{3}{7} times 2(4 - sqrt{2} )(4 + sqrt{2} ) = frac{6}{7} (16 - 2) = frac{6}{7} times 14 = 6 times 2 = 12$