Simultaneous equations, Graphing, Equation Solving

**Possessed_Little_Me** · Oct 25th 2008, 01:43 PM

heyy i need help urgently with these questions.

solve, set out clearly and write out each significant step of...
squared root of (x^2 - x) = 2 squared root of x - x (Hint: to start, square both sides) varify your solution.

A farmer wants to put some fish into his dam in March, and then sell them at the end of the growing season in November. Due to competition for available food, the amount that each fish gains in weight (w), is a function of the number of fish per cubic metre of water (n), and is given by the equation w= 60-25n where w is measured in grams... determine, with explanation, the number of fish per cubic metre of water that will maximise the total weight gain.

i have just asked a carpenter to supply me with two wooden cubes. The sides of both are an exact number of centimetres in length. The lager cube exeeds the smaller one in volume by 3185 cubic centimetres. How large is each cube? (Hint: use factors.)

anyone who can help me with these thank-you so much

~Laura~

**ajj86** · Oct 25th 2008, 02:34 PM

Note: sqrt = square root of

sqrt(x^2 - x) = 2*sqrt(x - x)
If you start by squaring both sides you get:

x^2 - x = 2^2 * (x - x)
x^2 - x = 4(x - x) But x - x = 0, So the right hand side of the equation is zero. You could have deduced this from the beginning, but the hint instructed that you start by squaring both sides, so I figured it would be better to follow those instructions.

So, we have x^2 - x = 0.

Factor out an x to get:

x(x-1) = 0.

The solutions are x = 0,1. I am extremely sorry for not noticing my mistake earlier.

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