Question

Volveré a subir estas y me iré lentamente no encerio gracias

Answer 1

1)

$x - y = 4 \: \: \ \: \: \: \: \: \: \: {x}^{2} + {y}^{2} = 58$

$(x - y) {}^{2} = 4 {}^{2} \\ {x}^{2} - 2xy + {y}^{2} = 16 \\ {x}^{2} + {y}^{2} - 2xy = 16 \\ 58 - 2xy = 16 \\ 2xy = 42 \\ xy = 21$

Clave: d)

2)

$P = \frac{(a + 3)(a + 4) + 2a}{(a + 6)(a + 2) + a} \\ P = \frac{ {a}^{2} + 7a + 12 + 2a}{ {a}^{2} + 8a + 12 + a} \\ P = \frac{ {a}^{2} + 9a + 12 }{ {a}^{2} + 9a + 12 } \\ P = 1$

Clave: a)

3)

i)

$A = (x + 3n)(x - 3n) + (x + n)(x - n) - 2(x + 2n)(x - 2n) \\ A = {x}^{2} - 9 {n}^{2} + {x}^{2} - {n}^{2} - 2( {x}^{2} - 4n {}^{2} ) \\ A = 2 {x}^{2} - 10 {n}^{2} - 2 {x}^{2} + 8n { }^{2} \\ A = - 2 {n}^{2}$

ii)

$B = (x + n)(x + 2n) + (x + 2n)(x + 3n) - 2(x + n)(x + 3n) \\ B = {x}^{2} + 3n + 2 {n}^{2} + {x}^{2} + 5n + 6 {n}^{2} - 2( {x}^{2} + 4n + 3 {n}^{2} ) \\ B = 2 {x}^{2} + 8n + 8 {n}^{2 } - 2 {x}^{2} - 8n - 6 {n}^{2} \\ B = 2 {n}^{2}$

iii)

$A + B = 2 {n}^{2} - 2 {n}^{2} \\ A + B = 0$

Clave: a)