Question

Find two numbers whose sum and product are 20 and 45 respectively

Answer 1

Answer:

two numbers are 10+√55 and 10-√55 whose sum and product are 20 and 45 respectively

Step-by-step explanation:

Let , one number is x

sum of two number is 20

then the another number is 20-x

product of the two numbers are 45

hence , x(20-x) =45 => 20x-x^2 =45 => x^2 -20x +45 = 0 =>

$x = ( -( - 20) + \sqrt({( - 20) { }^{2} } - 4 \times 45) ) \div 2$

and

$x = ( -( - 20) - \sqrt({( - 20) { }^{2} } - 4 \times 45) ) \div 2$

hence, x = (20+√(400-180))/2 and x =( 20 - √(400-180))/2

i.e. x = (20+2√55)/2 and x = (20-2√55)/2

i.e. x = 10+√55 and x = 10-√55

two numbers are 10+√55 and 10-√55 whose sum and product are 20 and 45 respectively