a = first number
b = second number
Conditions :
a * b = 10
a + b = 18
a + b = 18 Subtract a to both sides
a + b - a = 18 - a
b = 18 - a
a * b = 10
a * ( 18 - a ) = 10
18 a - a ^ 2 = 10
- a ^ 2 + 18 a = 10 Multiply both sides by - 1
a ^ 2 - 18 a = - 10 [ Add ( 18 /2 ) ^ 2 = 9 ^ 2 = 81 ] to both sides
a ^ 2 - 18 a + 81 = - 10 + 81
a ^ 2 - 18 a + 81 = 71
( a - 9 ) ^ 2 = 71
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Becouse :
( a - 9 ) ^ 2 = a ^ 2 - 2 a * 9 + 9 ^ 2 = a ^ 2 - 18 + 81
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( a - 9 ) ^ 2 = 71 Take square root to both sides
a - 9 = + OR - sqroot ( 71 ) Add 9 to both sides
a - 9 + 9 = 9 + OR - sqroot ( 71 )
a = 9 + OR - sqroot ( 71 )
The solutions are :
a = 9 - sqroot ( 71 )
and
a = 9 + sqroot ( 71 )
Now you have two set of solutions of this problem :
1 )
a = 9 - sqroot ( 71 )
b = 18 - a
b = 18 - [ 9 - sqroot ( 71 ) ]
b = 18 - 9 + sqroot ( 71 )
b = 9 + sqroot ( 71 )
2 )
a = 9 + sqroot ( 71 )
b = 18 - a
b = 18 - [ 9 + sqroot ( 71 ) ]
b = 18 - 9 - sqroot ( 71 )
b = 9 - sqroot ( 71 )
Final solutions :
1 )
a = 9 - sqroot ( 71 )
b = 9 + sqroot ( 71 )
2 )
a = 9 + sqroot ( 71 )
b = 9 - sqroot ( 71 )
Find two numbers (exactly) whose product is 10 and whose sum is 18.
3 answers
You want to find two numbers whose product is 10 and whose sum is 18.
So solution 1 and solution 2 are same solution.
The numbers are:
9 - sqroot ( 71 )
and
9 + sqroot ( 71 )
So solution 1 and solution 2 are same solution.
The numbers are:
9 - sqroot ( 71 )
and
9 + sqroot ( 71 )
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