) Let’s find the value of ab when a? + b2 = 52, a – b = 2​

Question

) Let’s find the value of ab when a? + b2 = 52, a – b = 2​

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Gianna 4 weeks 2021-08-17T10:03:01+00:00 1 Answer 0 views 0

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    2021-08-17T10:04:50+00:00

    Answer:a+b=6………………………………..(1)

    a-b=4…………………………………(2)

    Adding equation (1) and (2),we get,

    (a+b)+(a-b)=10

    => a+b+a-b=10

    => 2a=10

    => 2a/2=10/2

    => a=5

    Putting a=5 in equation (1),we get,

    5+b=6

    => b=6–5

    => b=1

    Now,

    a^2+b^2

    =(5)^2+(1)^2

    =25+1

    =26

    2nd Method:

    a+b=6

    On squaring both sides,

    (a+b)^2=(6)^2

    => a^2+2ab+b^2=36…………………….(1)

    a-b=4

    On squaring both sides,

    (a-b)^2=(4)^2

    =a^2–2ab+b^2=16……………..………….(2)

    Adding equation (1) and (2), we get,

    (a^2+2ab+b^2)+(a^2–2ab+b^2)=36+16

    => a^2+2ab+b^2+a^2–2ab+b^2=52

    => a^2+a^2+b^2+b^2+2ab-2ab=52

    => 2a^2+2b^2=52

    => 2(a^2+b^2)=52

    => a^2+b^2=52/2

    =>a^2+b^2=26

    Hence, a^2+b^2=26

    Step-by-step explanation:

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