sepia
Lv 7
sepia asked in Science & MathematicsMathematics · 2 years ago

How will you prove that (√(4 - √7) = (√(8 + 3√7) - 2√2))?

7 Answers

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  • 2 years ago
    Favorite Answer

    L.H.S.

    = (√(4 - √7))

    = (√7 - 1)/√2

    R.H.S.

    = (√(8 + 3√7) - 2√2))

    = (√7 - 1)/√2

    Hence LHS = RHS

  • 2 years ago

    4 - √7 = (1/2)(8 - 2√7) = (1/2)(7 - 2√7 + 1) = (1/2)(√7 - 1)^2

    √(4 - √7) = (1/√2)(√7 - 1)

    8 + 3√7 = (1/2)(16 + 2*3√7)/2 = (1/2)(7 + 2*3√7 + 9) = (1/2)(√7 + 3)^2

    √(8 + 3√7) - 2√2 = (1/√2)(√7 + 3) - (4/√2) = (1/√2)(√7- 1)

    Therefore

    √(4 - √7) = √(8 + 3√7) - 2√2

  • JOHN
    Lv 7
    2 years ago

    Answer

    Attachment image
  • atsuo
    Lv 6
    2 years ago

    Given equation : √(4 - √7) = √(8 + 3√7) - 2√2

    Both sides of given equation are positive ,

    so if [√(4 - √7)]^2 = [√(8 + 3√7) - 2√2]^2 then the given equation is proved .

    [√(4 - √7)]^2 = 4 - √7

    And

    [√(8 + 3√7) - 2√2]^2

    = 8 + 3√7 - 4√((8 + 3√7)*2) + 8

    = 16 + 3√7 - 4√(16 + 6√7)

    = 16 + 3√7 - 4√[(3 + √7)^2]

    = 16 + 3√7 - 4(3 + √7)

    = 4 - √7

    So , [√(4 - √7)]^2 = [√(8 + 3√7) - 2√2]^2 .

    Therefore , √(4 - √7) = √(8 + 3√7) - 2√2 .

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  • DWRead
    Lv 7
    2 years ago

    Parentheses are unbalanced

  • 2 years ago

    Work from one side to get to the other! In this case start from the right side and power both parts by two and do the math and I think you’ll end up with the other side! Just make sure to take the square root of the resault since you powered it by 2 in the beginning

  • alex
    Lv 7
    2 years ago

    What is (√(4 - √7) ?

    Is that (√(4 - √7))

    or

    √(4 - √7) ?

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