Question

Aratati ca ( a patrat+ b patrat) ( c patrat + d patrat) = (ac+bd) patrat + ( ad - bc) patrat oricare a fi a,b,c,d apartine R

Answer 1

Răspuns:

Explicație pas cu pas:

(a^2 + b^2)(c^2 + d^2) = a^2c^2 + a^2d^2 + b^2c^2 + b^2d^2

(ac + bd)^2 + (ad - bc)^2 = a^2c^2 + 2abcd + b^2d^2 + a^2d^2 - 2abcd + b^2c^2 = a^2c^2 + b^2d^2 + a^2d^2 + b^2c^2

rezulta ca (a^2 + b^2)(c^2 + d^2) = (ac + bd)^2 + (ad - bc)^2