If x = √3 − √2 , find the value of ( −1 )square 2

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If x = √3 − √2 , find the value of ( −1 )square 2

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Ruby 3 weeks 2021-09-09T16:01:11+00:00 1 Answer 0 views 0

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    2021-09-09T16:02:31+00:00

    Step-by-step explanation:

    ▪️Let √x – 1/√x = a

    ▪️Squaring both the sides,

    ▪️x + 1/x – 2 = a^2

    ▪️Putting the value,

    ▪️3–2√2 + 1/(3–2√2) – 2 = a^2

    ▪️a^2 = 1 – 2√2 + 1/(3–2√2)

    ▪️= [(3–2√2) (1–2√2) + 1] / 3–2√2

    ▪️= {3 – 8√2 + 9} / 3–2√2

    ▪️= [12 – 8√2] / 3–2√2

    ▪️Rationalising both the sides

    ▪️= {(12 – 8√2)(3+2√2)} ÷ (9–8)

    ▪️= 36 + 24√2 – 24√2 + 16(2)

    ▪️= 36 – 32

    ▪️=> 4

    ▪️a^2 = 4

    ▪️a = √4

    ▪️a = 2, -2

    ▪️So,

    ▪️√x – 1/√x = a = 2, -2.

    Hopes it help you❤️❤️

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