Question

value of
b ik x=3, y=-2 and =- L Find the
x-y12
x² + y² +
2²​

Answer 1

Answer:

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