Question

${x}^{2} + {y}^{2} = 58$
xy=21
a) x-y=?
b)
${x}^{2} - {y}^{2} =$
?
C) x+y=?​

Answer 1

Răspuns:

Explicație pas cu pas:

x²+y²=58, xy=21

a) (x-y)²=x²+y²=2xy=58-2·21=58-42=16. deci x-y=±√16=±4

c) (x+y)²=x²+y²+2xy=58+2·21=58+42=100, deci x+y=±√100=±10

b) x²-y²=(x-y)·(x+y)∈{-4·(-10); -4·10; 4·(-10); 4·10}={-40; 40}