Question

The sum of two numbers is 7/2 and their product is 3. What are the numbers?

Answer 1

AnsWer :

x = 2 , 3 / 2.

y = 2 , 3 / 2.

SolutioN :

Let, the number be x and y.

Case 1.

• The sum of two numbers is 7/2.

→ x + y = 7 / 2.

→ 2x + 2y = 7._______ ( 1 )

$\rule{90}2$

Case 2.

• their product is 3.

→ x * y = 3.______( 2 )

$\rule{90}2$

Taking Equation ( 2 )

→ x * y = 3.

→ y = 3 / x._______( 3 )

Now, Putting the value of y in Equation ( 1 )

→ 2x + 2y = 7.

→ 2x + 2( 3 / x ) = 7.

→ 2x² + 6 = 7x.

→ 2x² - 7x + 6 = 0.

Let Split the middle term.

→ 2x² - 7x + 6 = 0.

→ 2x² - 4x - 3x + 6 = 0.

→ 2x( x - 2 ) - 3( x - 2 ) = 0.

→ ( 2x - 3 )( x - 2 ) = 0.

Either,

→ x - 2 = 0.

→ x = 2.

Or,

→ 2x - 3 = 0.

→ 2x = 3.

→ x = 3 / 2.

Putting the value of x in Equation ( 3 )

→ y = 3 / x.

When, x = 2.

→ y = 3 / 2.

When, x = 3 / 2.

→ y = 3 // 3 / 2.

→ y = 3 / 1 * 2 / 3.

→ y = 2.

Therefore, the value of x is 2 , 3 / 2 and y = 3 / 2 and 2.