Question

It is given that x² - y² = 30 and x - y = 5. Find the value of (x + y)².

Answer 1

(x + y)² = 36

Explanation:

x² - y² ← is a difference of squares and factors as

(x - y)(x + y) , then

5(x + y) = x² - y² = 30 ( divide both sides by 5 )

(x + y) = 6 , then

(x + y)² = 6² = 36

Answer 2

36

Explanation:

when solving for two variables, we need to find one variable in terms of the other.

so, we can turn:

x - y = 5

into

x - y = 5

+ y + y

x = y + 5

Then, we can substitute "x" in the given equation with "y + 5"

x² - y² = 30

(y+5)² - y² = 30

(y + 5)(y + 5)

F: y² O: +5y I: +5y L: 25 {foil}

y² + 10y + 25 - y² = 30 {cancel y² - y²}

10y + 25 = 30

-25 -25

10y = 5

÷10 ÷10

y = 0.5

x = y + 5

x = 0.5 + 5

x = 5.5

check:

(5.5)² - (0.5)²

30.25 - 0.25 = 30

30 = 30

(TRUE)

now, we must find the value of:

(5.5 + 0.5)²

= (6)²

= 36

So, the value of (x + y)² is found to be 36

hope this helps!!