Question

daca x+y=10 xy=15 afla
a)x^2+y^2 b)x^4+y^4 (^) - inseamna la putere sa stiti sa
rezolvati

Answer 1

a) (x+y)²=10²=100
    (x+y)²=x²+2xy+y²
Deci x²+2xy+y²=100 <=> x²+30+y²=100 => x²+y²=70

b) (x²+y²)²=70²=4900
    (x²+y²)²=$x^{4}+ 2x^{2}y^{2} + y^{4}$
Deci $x^{4}+2 x^{2}y^{2} + y^{4}$=4900 <=> $x^{4} + 2* 15^{2}+ y^{4}$=4900 <=> $x^{4} +450+ y^{4}$=4900 => $x^{4} + y^{4}$=4450.

Answer 2

(x^2+y^2=(x+y)^2-2xy=100-30=70
(x^2+y^2)^2=x^4+y^4+2x^2y^2
4900=x^4+y^4+2ori225de unde
x^4+y^4=4900-450=4450