Question

1. calculaţi suma..a²+b²=?? stiind ca;
a+b=5
ab=15

2. a+b=??
ştiind ca..
a-b=10
a²-b²=40

3. a+b=9
a²+b²=81
a*b=?

Answer 1

$1) a + b = 5$

$ab = 15$

${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

${5}^{2} = {a}^{2} + 2 \times 15 + {b}^{2}$

$25 = {a}^{2} + 30 + {b}^{2}$

${a}^{2} + {b}^{2} = 25 - 30$

${a}^{2} + {b}^{2} = - 5$

$2)a - b = 10$

${a}^{2} - {b}^{2} = 40$

${a}^{2} - {b}^{2} = (a - b)(a + b)$

$(a - b)(a + b) = 40$

$10(a + b) = 40 \: | \div 10$

$a + b = 4$

$3)a + b = 9$

${a}^{2} + {b}^{2} = 81$

${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

${9}^{2} = 81 + 2ab$

$81 = 81 + 2ab$

$2ab = 81 - 81$

$2ab = 0 \: | \div 2$

$ab = 0$