Question

the product of two numbers is 120 the sum of their square is 289.the difference of two
numbers is ?

Answer 1

Solution :

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

The product of two numbers is 120 the sum of their square is 289.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The difference of two number.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Let the two numbers be R and M

A/q

$\mapsto\bf{RM=120....................(1)}$

&

$\sf{\bigg[Formula \:use\:a^{2} +b^{2} =(a-b)^{2} +2ab\bigg]}$

$\mapsto\sf{R^{2} +M^{2} =289}\\\\\mapsto\sf{(R-M)^{2}+2RM=289}\\\\\mapsto\sf{(R-M)^{2} +2(120)=289\:\:\:\:\:[from(1)]}\\\\\mapsto\sf{(R-M)^{2}+240=289}\\\\\mapsto\sf{(R-M)^{2}=289-240}\\\\\mapsto\sf{(R-M)^{2}=49}\\\\\mapsto\sf{R-M=\sqrt{49}} \\\\\mapsto\sf{\red{R-M=7}}$

Thus;

The difference of two number is 7.

Answer 2

Answer:

Given:

• The product of two numbers is 120 the sum of their square is 289.

Find:

• Find the difference of two number.

According to the question:

• 120 = Product of two numbers.

• 289 = Sum of the square.

• Let us assume 'x' and 'y' as two numbers.

• Well, according to the question [Sum of two numbers = 120] .•. [xy = 120].

Using formula:

⇒ a² + b² = (a - b)² + 2ab

Calculations:

⇒ x² + y² = 289 = (x - y)² + 2xy = 289

⇒ (x - y)² + 2 (120) = 289

⇒ (x - y)² + 240 = 289

⇒ (x - y)² = 289 - 240

⇒ (x - y)² = 49

⇒ x - y = √49

⇒ x - y = 7

⇒ xy = 7

Therefore, 7 is the difference between two numbers.