Question

If a,b and c are real numbers such that a^2 + 2b = 7, b^2 + 4c = -7 and c^2 + ab = -14.
Find a^2 + b^2 + c^2...

Answer 1

the answer is given as 14....but can anyone explain how?

Answer 2

You have three unknowns and three equations. You can use the substitution method to solve them.
Start by rearranging one equation for a single variable, say, b. I choose b because it is in the first equation and isn't squared:
\[a^2+2b=7\]
\[b=\frac{7-a^2}{2}\]

Now, where ever you see be in the second an third equation, replace it with the above.
You will then have two equations of two variables (b is gone).
Repeat with A or C and you will have one equation and one variable, solvable.

Answer 3

hhkkkk...!...hmm...I can try it out!

Answer 4

sweet, it should be good algebra practice

Answer 5

hey at the 2 eqns in the terms of a & c

are