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Advance Math

    0( √ ) (√ ) 1                                    मदद x – 1/x = 10 है, तत x³ – 1/x³ फयाफय

    [√ √ ] ,                               -         है:

    [ √ √ ][                 √]                      SSC CHSL 4 July 2019 IInd Shift

       [√ √ ]                                        (A) 970               (B) 1000

    [20x2 + 3y2 + 2√ -                               (C) 1030              (D) 1100

       ,-                                            Answer: (C)
    By comparing the coefficients 3
                                                     x – 1/x = 10

             ,√                                      Cube both side

                                                     x³ – 1/x³ – 3(x – 1/x) = 1000

             √)                                      x³ – 1/x³ = 1030

          = √ 9.                                     If (x – 7)³ + (x – 8)³ +(x + 6)³ = 3 (x – 7)
          =7
6. If a + b + c = 5 and a2 + b2 + c2 = 33,           (x – 8) (x + 6), then what is the value
          then what is the value of a3 + b3 + c3 –
          3abc?                                      of x?

          मदद a + b + c = 5 औय a2 + b2 + c2 = 33     अगय (x – 7)³ + (x – 8)³ +(x + 6)³ = 3 (x

                                                     – 7) (x – 8) (x + 6) है, तत x का भान क्मा

    है, तत a3 + b3 + c3 – 3abc का भान क्मा है?       है?

    SSC CHSL 3 July 2019 IIIrd Shift                 SSC CHSL 4 July 2019 IInd Shift

    (A) 195                   (B) 180                (A) 6                 (B) 8

    (C) 192                   (D) 185                (C) 10                (D) 3

    Answer: (D)                                      Answer: (D)

    a+b+c=5                                          (x – 7)3 + (x – 8)3 +(x – 6)3 = 3 (x – 7)

    Squaring both sides,                             (x – 8) (x + 6)

    a² + b² + c² + 2(ab + bc + ca) = 25              In these type of question go through

    33 + 2(ab + bc + ca) = 25                        options.

    ab + bc + ca = –4                                x=3

    a³ + b³ + c³ – 3abc = [a + b + c] [a² + b²       (3 – 7)3 + (3 – 8)3 +(3 + 6)3 = 3 (3 – 7)

    + c² – ab – bc – ca]                             (3 – 8) (3 + 6)

    a³ + b³ + c³ – 3abc = 5 [33 + 4]                 – 64 –125 + 729 = 3 (–4)(–5)(9)

    a³ + b³ + c³ – 3abc = 185                        540 = 540

7.  If a² + b² = 88 and ab = 6, (a > 0, b > 0)       Value of x = 3 satisfied.
    then what is the value of (a³ + b³) ?
                                                10.  If x4 + x–4 = 2207, (x > 0) then the

    अगय a² + b² = 88 औय ab = 6, (a > 0, b            value of x + x–1 is:

    > 0) है, तत (a³ + b³) का भान क्मा है?            अगय x4 + x–4 = 2207, (x > 0) है, तत x +

    SSC CHSL 4 July 2019 IInd Shift                  x–1 का

    (A) 980                   (B) 1180               भान है:

    (C) 820                   (D) 1000               SSC CHSL 4 July 2019 IInd Shift

    Answer: (C)                                      (A) 19                (B) 7

    a3 + b3 = [a + b] [a2 + b2 – ab]                 (C) 11                (D) 9

    [a + b]2 = a2 + b2 + 2ab                         Answer: (B)

    [a + b]2 = 88 + 2 × 6                            x4+1/x4=2207
    [a + b]2 = 100
    a + b = 10                                       Add 2 both side
    a3 + b3 = [a + b] [a2 + b2 – ab]
    = 10[88 –6]                                      x4+1/x4+2=2209x2+1/x2=47

                                                     Add 2 again in both side

                                                     x2+1/x2 + 2 = 49

    = 10 × 82                                        x+1/x=7
    = 820
                                                11.  If x4 + x–4 = 1442, (x > 0) then the

8. If x – 1/x = 10, then x³ – 1/x³ is equal          value of x - x–1 is:

    to:

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