Question

It is given that a + b = 6 and ab = 7.
(a) Find the value of a^2 + b^2. Can you do this without finding values for a and b?

Answer 1

@jim_thompson5910

Answer 2

why not?

Answer 3

what is \((a+b)^2\)

Answer 4

a^2 + 2ab + b^2

Answer 5

you know all you need

Answer 6

So (6)^2 = 36 and 2(7) = 14
because (a + b) = 6 and we have (a + b)^2
and ab = 7 and 2ab^2

Answer 7

There's a second part to this question where I need to make a geometry word problem which would have to correspond to the question in part (a).

Answer 8

Do you have any suggestions for what I should do?

Answer 9

probably draw a square with side \(a+b\) i guess

Answer 10

It's not clear whether or not you feel you have done the first part of this problem.

I'd suggest you experiment. Note that a^2 + b^2 is not a perfect square, but you can make it into an equivalent expression that containts a perfect square.

Suppose you begin with a^2 + b^2 and add 2ab to both sides:

a^2 +2ab + b^2 -2ab is the same, algebraically, as a^2 + b^2.

a^2 + 2ab + b^2 - 2ab = (a+b)^2 - 2ab.

But you know that a+b=6 and ab=7.

Substitute these knowns into (a+b)^2 - 2ab .

Answer 11

is this some time of math ed problem?

Answer 12

@satellite73 I am not sure what I am supposed to do w/ that square

Answer 13

fill in the areas

Answer 14

i meant that is my guess, not sure what else to do

Answer 15

Thank you so much! Can you help me with a couple of other problems?

Answer 16

i can try...