Question

if x+y= 6 and x - y = 4 find xy

Hint:4xy=(x+y)^2 -(x-y)^2


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Answer 1

Hey

Given :-

x + y = 6 ..... (1)

x - y = 4 ..... (2)

eq (1) + (2)

2x = 10

x = 10/2

x = 5

substitute x=5 in eq (1)

5 + y = 6

y = 6 - 5

y = 1

As we know the x and y values

xy = 5*1 = 5

OR

4xy = (x+y)^2 - (x-y)^2

4xy = (6)^2 - (4)^2

4xy = 36 - 16

4xy = 20

xy = 20/4

xy = 5

Answer 2

QUESTIONS:

If x + y = 6 & x - y = 4 , the find

(i) x² + y²

(ii) xy

GIVEN:

x + y = 6

x - y = 4

Hint: 4xy = (x + y)² - (x - y)²

SOLUTION:

Using the given hint

4xy = (x + y)² - (x - y)²

Substituting the value of x + y & x - y

→ 4xy = 6² - 4²

→ 4xy = 36 - 16

→ 4xy = 20

→ xy = 20/4

→ xy = 5

→ xy = 5

$\rule{110}1$

Finding x² + y²

Using

a² + b² = (a + b)² - 2ab

Similarly

x² + y² = (x + y)² - 2xy

Substituting the values of x + y & xy

→ x² + y² = 6² - 2(5)

→ x² + y² = 36 - 10

→ x² + y² = 26

→ x² + y² = 26

Hence, xy = 5 & x² + y² = 26

$\rule{110}2$