2. If `x+y = 5` and `xy = 6`, then find `x^2+y^2`
Solution:
Here `x+y=5 and xy=6`
Now, We know that
`x^2+y^2=(x+y)^2-2 xy`
`:.x^2+y^2=5^2-2*6`
`:.x^2+y^2=25-12`
`:.x^2+y^2=13`
2. If `x+y=5` and `xy=6`, then find `x^2-y^2`
Solution:
Here `x+y=5 and xy=6`
Now, We know that
`(x-y)^2=(x+y)^2-4 xy`
`:.(x-y)^2=5^2-4*6`
`:.(x-y)^2=25-24`
`:.(x-y)^2=1`
`:.x-y=1`
Now, We know that
`x^2-y^2=(x-y) (x+y)`
`:.x^2-y^2=1*5`
`:.x^2-y^2=5`
2. If `x+y=3` and `x-y=15`, then find `x^2+y^2`
Solution:
Here `x+y=3` and `x-y=15`
Now, We know that
`4 xy=(x+y)^2-(x-y)^2`
`:.4 xy=3^2-15^2`
`:.4 xy=9-225`
`:.4 xy=-216`
`:.xy=-216/4`
`:.xy=-54`
Now, We know that
`x^2+y^2=(x+y)^2-2 xy`
`:.x^2+y^2=3^2-2*-54`
`:.x^2+y^2=9--108`
`:.x^2+y^2=117`
2. If `x+y=3` and `x-y=15`, then find `x^2-y^2`
Solution:
Here `x+y=3` and `x-y=15`
Now, We know that
`x^2-y^2=(x-y) (x+y)`
`:.x^2-y^2=3*15`
`:.x^2-y^2=45`
2. If `x+y=3` and `x-y=15`, then find `x^3-y^3`
Solution:
Here `x+y=3` and `x-y=15`
Now, We know that
`4xy=(x+y)^2-(x-y)^2`
`:.4xy=3^2-15^2`
`:.4xy=9-225`
`:.4xy=-216`
`:.xy=-216/4`
`:.xy=-54`
Now, We know that
`x^3-y^3=(x-y)^3+3xy(x-y)`
`:.x^3-y^3=15^3+3*(-54)*15`
`:.x^3-y^3=3375-2430`
`:.x^3-y^3=945`
This material is intended as a summary. Use your textbook for detail explanation.
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