Algebraic Solution of System of Equation involving quadratic

Question

The sum of two number is 10 their product is 20. Find the numbers.
I need a clear solution :)

Answer 1

Hi Yhan,

 

Let two nos be x & y.

 

x+y = 10......eqn 1

 

x*y = 20.......eqn 2

 

now from eqn 1, y=10-x

 

substituting value of y in eqn 2, we get

 

x*(10-x) = 20

10x-x² =20

x² -10x +20 =0

 

 quadratic eqn: ax² +bx + c= 0 is x = -b ±√ b² -4ac /2a

using this formula,

a=1,b=-10, c=20.

 

x = 10 ±√ 100-80  /2

x = 10±√20 /2

x = 10±2√5 /2

 

x =2(5±√5) /2

 

x= 5+√5 0r x= 5 -√5

so if x = 5 + √5, then y = 10- (5+√5)= 5-√5

 

 if x= 5-√5 ,then y=10 - (5-√5) = 5 + √5

 

two numbers are 5 + √5 & 5 - √5