If x =√3-√2/√3+√2 y=√3+√2/√3-√2 so what is the value of x²+y²+xy

Question

If x =√3-√2/√3+√2 y=√3+√2/√3-√2 so what is the value of x²+y²+xy

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Ximena 5 months 2022-01-06T17:51:38+00:00 2 Answers 0 views 0

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  1. Skylar
    0
    2022-01-06T17:53:18+00:00
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    Answer:

    We have, x = (√3 – √2 )/(√3 + √2) and y = (√3 + √2) / (√3 – √2)

    On rationalising the denominator of x :

    X = (√3 – √2 ) × (√3 – √2) /(√3 + √2) (√3 – √2)

    x = (√3 – √2)² / (√3 + √2) (√3 – √2)

    By Using Identity : (a – b)² = a² + b² – 2ab & (a + b)(a – b) = a² – b²

    x = {√3² + √2² – 2 × √3 × √2}/ √3² – √2²

    x = {3 + 2 – 2√6}/( 3 – 2)

    x = 5 – 2√6 ………..(1)

    Now ,

    x² = (5 – 2√6)²

    By Using Identity : (a – b)² = a² + b² – 2ab

    x² = 5² + (2√6)² – 2 × 5 × 2√6

    x² = 25 + 24 – 20√6

    x² = 49 – 20√6 …………(2)

    On rationalising the denominator of y :

    y = (√3 + √2) × (√3 + √2)/ (√3 – √2) × (√3 + √2)

    y = (√3 + √2)²/(√3 – √2) × (√3 + √2)

    By Using Identity : (a + b)² = a² + b² + 2ab & (a + b)(a – b) = a² – b²

    y = {√3² + √2² + 2 × √3 × √2}/ √3² – √2²

    y = {3 + 2 + 2√6}/( 3 – 2)

    y = 5 + 2√6 …………(3)

    Now ,

    y² = (5 + 2√6)²

    By Using Identity : (a + b)² = a² + b² + 2ab

    y² = 5² + (2√6)² + 2 × 5 × 2√6

    y² = 25 + 24 + 20√6

    y² = 49 + 20√6 …………(4)

    Now,

    From eq 1 & 3 :

    xy = (5 – 2√6) ( 5 + 2√6)

    By Using Identity : (a + b)(a – b) = a² – b²

    xy = 5² – (2√6)²

    xy = 25 – 24

    xy = 1 …………(5)

    Therefore , x² + xy + y²

    From eq 2, 4 & 5 :

    = 49 – 20√6 + 1 + 49 + 20√6

    = 49 + 49 + 1

    = 99

    x² + xy + y² = 99

    Step-by-step explanation:

    hope it helps plz mark as brainlist

  2. Skylar
    0
    2022-01-06T17:53:35+00:00
    Reply

    Answer:

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