If a + b = 8 and ab = 15 then, find
a⁴ + 2a²b + b⁴ - a²b²
Answers
Hey there!
Given:
a + b = 8
ab = 15
To find :
a4 + a²b2 + b4
Proof:
ab = 15
=> b = 15/a ( Equation 1)
Substituting this in a + b = 8 we get,
=> a + 15/a = 8
=> a2 + 15 / a = 8
=> a 2 + 15 = 8a
=> a2 - 8a + 15 = 0
Solving for'a 'we get,
=> a 2 - 5a - 3a + 15 = 0
=> a (a - 5)- 3 ( a - 5) = 0
=> (a -3)( a -5) = 0
=> a = 3,5
So b = 15/a
=> b = 15 / 5 if a = 5
=> b = 3 if a = 5
If a = 5 then b = 15/5 = 3
So a and b have both interchangeable
values of 3 and 5.
So If we consider a = 3 and b = 5 we get,
=>
=> 34 + 32.52 + 54
=> 81 + 9.25 + 625
=> 81 +225 + 625
=> 931
If we take a = 5 and b = 3 we get
=> 54 + 52.32+ 34
625 + 25.9 + 81
625 +225 + 81
=> 931
Hence in both cases we get 931.
Hence a4 +a? b2 + b4 = 931, where a and
b= 5 and 3.
Hope my answer helped !
Given:
a+b=8
ab = 15
To find:
a4 + 2a²b + b4
Proof:
ab = 15
=> b= 15/a ( Equation 1)
Substituting this in a + b = 8 we get,
=> a+ 15/a = 8
=> a2 + 15/a=8 => a 2 + 15 = 8a
=> a2 - 8a+ 15 = 0
Solving for a 'we get,
=> a 2-5a - 3a + 15 = 0
=> a (a - 5)- 3 ( a -5) = 0
=> (a -3)( a -5) = 0
=> a = 3,5
So b = 15/a
=> b= 15/5 if a = 5
=> b=3 if a = 5
If a = 5 then b = 15/5 = 3
So a and b have both interchangeable
values of 3 and 5.
So If we consider a = 3 and b = 5 we get,
=>
=> 34 + 32.52 + 54
=> 81 + 9.25 + 625
=> 81 +225 + 625
=> 931
If we take a = 5 and b = 3 we get
=> 54 + 52.32+ 34
625+25.9 + 81
625 +225 + 81
=> 931