Question

Se x+y=15 e xy=54, qual é o valor de x²+10xy+y² ?​

Answer 1

Vamos là.

x + y = 15

xy = 54

x² + 10xy + y²

(x + y)² = 15² = 225

x² + 2xy + y² = 225

x² + y² = 225 - 2*54 = 117

x² + 10xy + y² = 117 + 10*54 = 657

Answer 2

$> \: resolucao \\ \\ \geqslant sistema \: de \: equacao \: do \: 2 \: grau \\ \\ x + y = 15 > x = 15 - y \\ xy = 54 \\ \\ (15 - y)y = 54 \\ 15y - y {}^{2} = 54 \\ - y {}^{2} + 15y - 54 = 0 \times ( - 1) \\ y {}^{2} - 15y + 54 = 0 \\ \\ delta = ( - 15) {}^{2} - 4.1.54 \\ delta = 225 - 216 \\ delta = 9 \\ delta = \sqrt{9} \\ delta = + - 3 \\ \\ \\ y = \frac{15 + 3}{2} \\ y = \frac{18}{2} \\ y = 9 \\ \\ x = 15 - y \\ x = 15 - 9 \\ x = 6 \\ \\ \\ s \: > \: ( \: \: x = 6 \: \: e \: \: y = 9 \: \: ) \\ \\ = = = = = = = = = = = = = = = = = \\ \\ > valor \: da \: expressao \: {x}^{2} + 10xy + y {}^{2} \\ \\ = x {}^{2} + 10xy + {y}^{2} \\ = 6 {}^{2} + 10.6.9 + 9 {}^{2} \\ = 36 + 540 + 81 \\ = 657 \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant \geqslant \geqslant$