SOLUTION: The difference of two numbers is 2 and the sum of their square twenty what are the numbers
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Question 990548: The difference of two numbers is 2 and the sum of their square twenty what are the numbers
Found 2 solutions by ikleyn, macston:
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
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Answer. a) 4 and 2; b) -2 and -4.
Solution
x - y = 2; ----->
= , ----->
= 4, (recall that ) ----->
= , ----->
2xy = 20 - 4 = 16, ----->
xy = = 8. ----->
. ----->
x = 2+y ----->
(2+y)*y = 8, ----->
= ----->
The roots are = 2, = -4 (use the quadratic formula or the Viete's theorem). ----->
The solutions are (x,y) = (4.2) and (x,y) = (-2, -4).
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
x and y are the two numbers
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x-y=2 or y-x=2 (order is not specified)
x=2+y or x=2-y
.
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For y=-4:
x=y+2=-4+2=-2
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CHECK:
x^2+y^2=20
(-4)^2+(-2)^2=20
16+4=20
20=20
.
For the first solution the difference between first and second:
x-y=2
-2-(-4)=2
-2+4=2
2=2
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ANSWER 1: One solution is (-2,-4)
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For y=2:
x=y+2=2+2=4
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CHECK:
x^2+y^2=20
2^2+4^2=20
4+16=20
20=20
.
For second solution the difference between second and first:
y-x=2
4-2=2
2=2
.
ANSWER 2: Another solution is 2,4
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