Question

if 2xy = 864 and x²-y² = 252 find x+y

Answer 1

You can use the identity (x-y)square = x square + y square - 2ab

Answer 2

Answer:

x+y=42

Step-by-step explanation:

Given: $2xy = 864$  and $x^2-y^2=252$

We need to find the value of x+y

Let x+y=k

$x^2-y^2=(x+y)(x-y)$

$x-y=\sqrt{(x+y)^2-4xy}$

$(x+y)\sqrt{(x+y)^2-4xy}=252$

$2xy=864\Rightarrow 4xy=1728$

Therefore, we get an equation

$k\sqrt{k^2-1728}=252$

Now we solve for k

Taking square both sides

$k^4-1728k^2-63504=0$

Using quadratic formula calculator we get k=42

Hence, The value of x+y=42