Question

The sum of squares of two numbers is 90and the square of their difference is 46 the product of the two numbers is what

Answer 1

let the two numbers are x , y


sum of squares = 90

x^2 + y^2 = 90

square of their difference = 46

(x - y)^2 = 46


x^2 + y^2 - 2xy = 46


90 - 2xy = 46


2xy = 44


xy = 22


product of two numbers = 22


Answer: product = 22

Answer 2

Product of numbers is 22.

Given:

• The sum of squares of two numbers is 90,and
• The square of their difference is 46.

To find:

• Find the product of the two numbers.

Solution:

Concept to be used:

1. Assume the two numbers.
2. Write equations from the statements.
3. Find the product of two numbers.

Step 1:

Write the equations.

Assume the numbers first.

Let first number is 'x' and second is 'y'.

ATQ,

$\bf {x}^{2} + {y}^{2} = 90...eq1$

and

$\bf ( {x - y)}^{2} = 46...eq2$

Step 2:

Find the product of two numbers.

Open Identity $\bf ( {a-b)}^{2} = {a}^{2} + {b}^{2} - 2ab$

so,

${x}^{2} + {y}^{2} - 2xy = 46$

put the value of x²+y² from eq 1.

$90 - 2xy = 46$

or

$- 2xy = 46 - 90$

or

$- 2xy = - 44$

or

$2xy = 44$

or

$\bf xy = 22$

Thus,

Product of both numbers is 22.

#SPJ3

Learn more:

1)Find two numbers whose sum and product are 20 and 96 respectively

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2) The sum of two numbers is 22 and the sum of their squares is 250. Find the numbers.

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