Elementary Algebra

  1. If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 ?
    1. -1
    2. 0
    3. 1
    4. 2
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    x = 1 + √2
    ∴ x4 - 4x3 + 4x2 = x2(x2 - 4x + 4)
    = x2(x - 2)2
    = (1 + √2)2(1 + √2 - 2)2

    Correct Option: C

    x = 1 + √2
    ∴ x4 - 4x3 + 4x2 = x2(x2 - 4x + 4)
    = x2(x - 2)2
    = (1 + √2)2(1 + √2 - 2)2
    =(√2 + 1)2 (√2 - 1)2
    =[(√2)2 - (1)2]2
    =(2 - 1)2 =1

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  1. What is the solution of the equations x - y = 0.9 and 11(x + y)-1 = 2 ?
    1. x = 3.2, y = 2.3
    2. x = 1, y = 0.1
    3. x = 2, y = 1.1
    4. x = 1.2, y = 0.3
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    x - y = 0.9 ...(i)
    and 11(x + y)-1=2
    ⇒ 11/ (x + y) = 2
    ⇒ 2(x + y) =11

    Correct Option: A

    x - y = 0.9 ...(i)
    and 11(x + y)-1=2
    ⇒ 11/ (x + y) = 2
    ⇒ 2(x + y) =11
    ⇒ x + y = 11/2 ...(ii)
    On solving Eqs.(i) and (ii),we get
    x = 3.2
    and y = 2.3

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