Question

if x-y =8 and xy= 5 find x^2+y^2

Answer 1

Square the both sides of(x-y)²
(x-y)²=(8)²
x²+y²-2xy=64
x²+y²-2*5=64(since:-xy=5)
x²+y²-10=64
x²+y²=64+10
x²+y²=74

Answer 2

Concept:

Algebraic Identities. some of the algebraic identities are given below,

1. (a + b)² = a² + b² + 2ab, where a and b are two variables.

2. (a - b)² = a² + b² - 2ab, where a and b are two variables.

3. (a - b)(a + b) = a² - b², where a and b are two variables.

Given:

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

xy = 5                   ---------------------- (ii)

Find:

The value of x² + y².

Answer:

x² + y² = 74

Solution:

Taking (i), we have

x - y = 8

Squaring both sides, we get

(x - y)² = 8²

Using Identity number 2., we have

x² + y² - 2xy = 64

But from (ii), we have xy = 5.

Putting the value of xy, we get

x² + y² - 2(5) = 64

x² + y² - 10 = 64

x² + y² = 64 + 10

x² + y² = 74

Hence, the value of x² + y² is 74.

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