Question

The sum of two numbers is 25 and their product is 144. Find the numbers

Answer 1

Answer:

So the difference is 7.

Step-by-step explanation:

Let the numbers be x & y .

Product is 25

xy = 144 .

Sum is 25 .

x + y = 25 .

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

( 25 )^2 = x^2 + 2 ( 144 ) + y^2

625 = x^2 + y^2 + 288

x^2 + y^2 = 625 - 288 .

x^2 + y^2 = 337 .

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

( x - y )^2 = 337 - 288

( x - y )^2 = 49

( x - y ) = 7

So the difference is 7.

Answer 2

9, 16

Step-by-step explanation:

Let x, y are numbers sum = 25 and product =144

Let the two numbers are x and y, then by

hypothesis,

x+y=2-------------Eqavation 1

and xy=144

∴(x−y)2=(x+y)2−4xy

=(25)2−4×144

=625−576=49

Hence (x−y)2=49

(x−y)=±7------------Eqavation 2

Eqa.1 + Eqa.2

2x = 25 + 7 = 32

x = 32/2 =16

y = 25 - 16 =9