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THE DIFFERENCE OF TWO NUMBERS IS TWO. IF THE SUM OF THEIR SQUARES IS TWENTY, WHAT ARE THE TWO NUMBERS

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HuInDWorldviz
Let x² + y² = 20.
[tex] x^{2} + y^{2} = 20 \\ 16 + 4 = 20 \\ \sqrt{16} = 4 \\ \sqrt{4} = 2 \\ 4 - 2 = 2[/tex]

The two numbers are 2 and 4.
Ihartangelviz
a-b=2
a=2+b

a²+b²=20
(2+b)²+b²=20
4+4b+b²+b²=20
4+4b+2b²=20
2b²+4b-16=0
b²+2b-8=0
(b+4)(b-2)=0
b+4=0     b-2=0
b=-4        b=2
if b=-4
a=2+b
 =2+(-4)
=-2

if b=2
a=2+b
 =2+2
 =4

if b=-4 and a=-2 then,
a²+b²=20
(-2)²+(-4)²=20
16+4=20
20=20

a-b=2
(-2)-(-4)=2
2=2

if b=2 and a=4
a²+b²=20
(4)²+(2)²=20
16+4=20
20=20

a-b=2
4-2=2
2=2

therefore, 
a=4   while b=2
or
a=-2 while b=-4

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