Question

if x+y=8 and xy=15 then
$x {}^{2} + y {}^{2} =$
​

Answer 1

Step-by-step explanation:

Given that,

x + y = 8 --------(i)

and xy = 15

Now, On squaring both sides of the equation (i)

We get,

(x + y )² = 8²

=> x² + 2xy + y² = 64

[(a + b)² = a² + b² +2ab]

=>x² + y² = 64 - 2xy

Putting the value of xy = 15

=>x² + y² = 64 - 2*15

=>x² + y² = 64 - 30

=>x² + y² = 34

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Answer 2

Answer:

34

Step-by-step explanation:

Given:

x + y = 8 and xy = 15

To Find:

x² + y² = ?

Solution:

∴ (x + y )² = x² + y² + 2xy

x² + y² = (x + y )² - 2xy

==>  8² - 2 * 15

==>  64 - 30

==> 34

Result:

x^2 + y^2 = 34