1. ## algebra help

1) If the average (arithmetic mean) of five consecutive integers is m, what is the product of the greatest and least of these five integers?

2) If x + y = 11 and xy = 15, find the value of x^2 + y^2.

3) Find the solution to absolute vavalue of (x ) - 1 = 2x + 1.

2. Originally Posted by sri340
1) If the average (arithmetic mean) of five consecutive integers is m, what is the product of the greatest and least of these five integers?

2) If x + y = 11 and xy = 15, find the value of x^2 + y^2.

3) Find the solution to absolute vavalue of (x ) - 1 = 2x + 1.
1) $\frac{n_1 + n_2 + n_3 + n_4 + n_5 }{5} = m$

$n_1 = n_1$
$n_2 = n_1 + 1$
$n_3 = n_2 + 1 = n_1 + 2$
$n_4 = n_1 + 3$
$n_5 = n_1 + 4$

$\frac{n_1 + n_1 + 1 + n_1 + 2 + n_1 + 3 + n_1 + 4 }{5} = m$

$\frac{5n_1 + 10 }{5} = m$

$n_1 + 2 = m$

$n_1 = m - 2$

$n_5 = n_1 + 4 = m - 2 + 4 = m + 2$

$n_1*n_5 = ( m - 2 )( m + 2 ) = m^2 - 4$

2) $x + y = 11$

$( x + y )^2 = 11^2$

$x^2 + 2xy + y^2 = 121$

$xy = 15$

$x^2 + 2*15 + y^2 = 121$

$x^2 + y^2 = 91$

3)

$|x| - 1 = 2x + 1$

a) if $x \geq 0$

$|x| = x$

$x - 1 = 2x + 1$

$x = -2$

but $x \geq 0$

so this is not a solution

b) if $x < 0$

$|x| = -x$

$-x - 1 = 2x + 1$

$3x = -2$

$x = -\frac{2}{3}$