## 1. If a + b = 15 and a – b = 13. then the value of a square + b square is​

Question

1. If a + b = 15 and a – b = 13. then the value of a square + b square is​

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2 weeks 2021-11-15T10:18:42+00:00 2 Answers 0 views 0

Step-by-step explanation:

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

=> a² + 15 = 8a

=> a² – 8a + 15 = 0

Solving for ‘ a ‘ we get,

=> a² – 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 + a². b² + b⁴ = 931, where a and b = 5 and 3.

2. Step-by-step explanation:

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