Verified answer

( x + y ) = 7

squaring on both sides

( x + y )^2 = 7^2

x^2 + y^2 + 2xy = 49

x^2 + y^2 + 2 ( - 18 ) = 49

x^2 + y^2 - 36 = 49

x^2 + y^2 = 49 + 36

x^2 + y^2 = 85

x= -2

y= 9

-2 + 9 = 7

(9)(-2) -> 9 * -2 = -18 negative multiplied by a positive = negative

9^2 -> (9 * 9) =81

-2^2 -> (-2 * -2) = 4 negative multiplied by a negative = positive

4+81 = 85

For future reference, just remember this, don't get scared of letters, the letters are just there to let you know that you are dealing with different numbers that need their values found, such as in this case "x" and "y".

When you work math problems, once you find the value (the number) of a letter, the value of that letter will never change.

Such as in this case, what 2 numbers go into 7? 2+5, 1+6, 3+4.

But when the 2 letters are MULTIPLIED we have a NEGATIVE number so that means one of the letters "x" or "y" is a negative.

Well to help us find out number is subtracting the other unknown number, they showed "x" multiplied by "y" equals.

-18.

So what 2 numbers multiplied = 18? 3*6, and 2*9.

Well guess what if you take 2 away from 9 that = 7

So 2 is the negative number.

This should help you out in future problems.

Now if you want to CUT DOWN ON YOUR WORK

remember this:

Even numbers are 0,2,4,6,and 8

Odds are 1,3, 5,7, and 9

even + even = even

Proof: 2+22 = 24

odd + odd = even

Proof: 23 + 3 = 26

odd +even = odd

Proof: 23 + 4 = 27

Multiplying is a little different

even * even = even

Proof: 4 * 4 = 16

EVEN * ODD = EVEN

Proof : 4 * 3 = 12

ODD * ODD = ODD

Proof: 3 * 3 = 9

This will help you make sure you have the correct final answer and cut down on your work by expecting what kind of number to come out and how to find the unknown numbers.

Solution:

x+y=7

Squaring both sides we get

(x+y)² =(7)²

x²+y² +2xy=49 (shift + 2xy to right side and when we change sides,sign changes)

x²+y²=49-2xy (put the value of xy)

x²+y²=49-2(-18) (multiply -2 with -18)

x²+y²=49+36 (just add)

x²+y²=85 (your answer)

Hope i helped

>>(x+y)² = x² +y² + 2xy

>>x² + y² = (x+y)² - 2xy

>>x²+y² = (7)² -2(18)

>>x²+y² = 85

Why did u ask such a question??