Question

Scrieti ca patrat al unei sume:
29+12√5=
calculati:
a) (√45-√5)²-(√11-√13)*(√11+√13)=

vva rog urgent avem evaluare

Answer 1

A)

$( \sqrt{45} - \sqrt{5} ) {}^{2} - ( \sqrt{11} - \sqrt{13} )( \sqrt{11} + \sqrt{13} ) = \\ (3 \sqrt{5} - \sqrt{5} ) {}^{2} - (11 - 13) \\ (2 \sqrt{5} ) {}^{2} - ( - 2) \\ 4 \times 5 + 2 \\ 20 + 2 \\ 22$

Succes....)

Answer 2

$\it 29+12\sqrt5= (3+2\sqrt5)^2$

$\it \sqrt{45}=\sqrt{9\cdot5}=3\sqrt5\\ \\ (3\sqrt5-\sqrt5)^2-(\sqrt{11}-\sqrt{13})(\sqrt{11}+\sqrt{13})=\\ \\ =(2\sqrt5)^2 -[(\sqrt{11})^2-(\sqrt{13})^2] =4\cdot5-(11-13) =20-(-2)=22$