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

Answers ( )

    0
    2021-11-15T10:20:09+00:00

    Answer:

    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.

    0
    2021-11-15T10:20:27+00:00

    Step-by-step explanation:

    okk yess right hai na y wrong hai

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