Question

Determinati numerele rationale a si b pentru care avem:

$a( 3\sqrt{2} -2)=b( 5\sqrt{2} -3)= 3\sqrt{2}-1$

Answer 1

a(3√2-2)=3√2-1
a=(3√2-1)/(3√2-2)=(3√2-1)(3√2+2)/(3√2-2)(3√2+2)=
=(9×2-3√2+6√2-2)/(9×2-4)=(16+3√2)/14


b(5√2-3)=3√2-1
b=(3√2-1)/(5√2-3)=(3√2-1)(5√2+3)/(5√2-3)(5√2+3)=
=(15×2-5√2+9√2-3)/(25×2-9)=(27+4√2)/41