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long division with remainder 125/6

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x²+y²=1, (x−0.5)²+(y−0.5)²=0.25

Solution

(

`x`=√1−8+5√1.7516 ,	`y`=2.5+√1.754
`x`=√1−8−5√1.7516 ,	`y`=2.5−√1.754

)

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Solution steps

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[

x²+y²=1

(x−0.5)²+(y−0.5)²=0.25

]

Isolate x for x²+y²=1: x=√1−y², x=−√1−y²

Plug the solutions x=√1−y², x=−√1−y² into (x−0.5)²+(y−0.5)²=0.25

For (x−0.5)²+(y−0.5)²=0.25, subsitute x with √1−y²: y=2.5+√1.754 , y=2.5−√1.754

For (x−0.5)²+(y−0.5)²=0.25, subsitute x with −√1−y²: No Solution for y∈ℝ

Plug the solutions y=2.5+√1.754 , y=2.5−√1.754 into x²+y²=1

For x²+y²=1, subsitute y with 2.5+√1.754 : x=√1−8+5√1.7516 , x=−√1−8+5√1.7516

For x²+y²=1, subsitute y with 2.5−√1.754 : x=√1−8−5√1.7516 , x=−√1−8−5√1.7516

Verify solutions by plugging them into the original equations

Therefore, the final solutions for x²+y²=1, (x−0.5)²+(y−0.5)²=0.25 are

(

`x`=√1−8+5√1.7516 ,	`y`=2.5+√1.754
`x`=√1−8−5√1.7516 ,	`y`=2.5−√1.754

)

Long Division with Remainder Examples

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

long division with remainder 125/6

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