Question

Factorisation of algebraic expressions :
• If x2 + y2 = 80 and xy = 12 , find the value of ( x - y )2 .

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Answer 1

Answer:

4

If x²＋y²=80 and xy=12 , how do we find the value of (x-y) ²?

Lukas Schmidinger

Answered March 31, 2019

If x²＋y²=80 and xy=12 , how do we find the value of (x-y) ²?

(x−y)2=x2−2xy+y2=x2+y2−2xy

And we know x2+y2 as well as xy

So it is

80−2×12=80−24=56

By the way:

xy=12⟹x=12y

Therefore

x2+y2=80

can be transformed to

y4−80y2+144=0

Which with z=y2

Can be solved as quadtric equation:

z=−(−80)±(−80)2−4⋅1⋅144√2⋅1=40±491−−√

So

y=±210+91−−√−−−−−−−−√

So

x=12±210+91√√=

±610+91√√=

±610+91√√10±91√=

±610+91√√⋅(10∓91√)9=

±6010+91√√∓610⋅91√+91√9=

±2010+91√√∓210⋅91√+91√3

Answer 2

Answer:

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Step-by-step explanation:

$we \: \: know \: \: that \\( {x} - {y})^{2} = {x}^{2} + {y}^{2} - 2xy \\ \\ putting \: \: values, \: \: we \: \: get \\ ( {x} - {y})^{2} = 80 - 2(12) \\ ( {x} - {y})^{2} =80 - 24 \\ ( {x} - {y})^{2} =56$