# Thread: algebra help

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) $\displaystyle \frac{n_1 + n_2 + n_3 + n_4 + n_5 }{5} = m$

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

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

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

$\displaystyle n_1 + 2 = m$

$\displaystyle n_1 = m - 2$

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

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

2) $\displaystyle x + y = 11$

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

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

$\displaystyle xy = 15$

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

$\displaystyle x^2 + y^2 = 91$

3)

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

a) if $\displaystyle x \geq 0$

$\displaystyle |x| = x$

$\displaystyle x - 1 = 2x + 1$

$\displaystyle x = -2$

but $\displaystyle x \geq 0$

so this is not a solution

b) if $\displaystyle x < 0$

$\displaystyle |x| = -x$

$\displaystyle -x - 1 = 2x + 1$

$\displaystyle 3x = -2$

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