Sum of Algebra

Sum of Algebra 

The collection of Sum of Algebra of different competitive exams is given here.

1) If  {a}^x =  b, {b}^x =c  and  {c}^x = a then find the value of xyz.
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2) If a+b+c = 9 and  ab+bc+ca = 40 then find the value of {a}^2+{b}^2+{c}^2.
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3) If a+b=7 then find the value of {(a-b)}^2 +4ab+ 1 .
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4) If 2x+y = 3  and xy = 1 then find the value of {(x+y)}^{x-y}
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5) If   x = (b-c) (a-d),  y = (c-a) (b-d) and z = (a-b) (c-d) then find the value of {x}^3 + {y}^3 +{z}^3 .
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6) If {(a-2)}^2 + {(b+3)}^2 + {(c-4)}^2 = 0 then find the value of   a-b+c
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7) If {(x)}^2+{(y)}^2+4x+4y+8 =0 then find the value of x+y .
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8) If a+b+c = 0,then find the value of {a}^2(b+c) + {b}^2 (c+a) + {c}^2 (a+b) .
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9) If a+b+c = 13, and ab+bc+ca = 50 then find the value {a}^2 +{b}^2 +{c}^2.
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10) If p+q = r and pqr = 30 then find the value of {p}^3 + {q}^3 - {r}^3.
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11) If {x}^2+8{y}^2+9{z}^2 - 4xy - 12xz = 0, then which option is correct.
a) 3x = 2y = z
b) x=y=z
c) x=2y=z
d) x+2y+3z=0
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12) If {3}^{(x-y)} = 27, and {3}^{(x+y)} = 243, then find the value of x.
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13) If x = 12 and y = 4 then find the value of {(x+y)} ^{x/y} .
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14) If {(a-1)}^2 + {(b+2)}^2 + {(c+1)}^2 = 0, then find the value of 2a+3b+7c.
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15) If p = 124 then \sqrt [ 3 ]{ p({ p }^{ 2 }+3p+3)+1 } = ?.
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16) {x}^a.{x}^b.{x}^c = 1 then find the value of {a}^3 +{b}^3+{c}^3.

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17) If (x+y+z) = 16 and (xy+yz+zx) = 78 then find the value of {x}^3+{y}^3+{z}^3 -3 xyz.
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18) If {a}^2 + {b}^2 + 4{c}^2 = 2(a+b-2c) – 3 and a,b,c are real numbers then find the value of ({a}^2+{b}^2+{c}^2).
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19) If {a}^2 +1 =a, then find the value of {a}^{12} + {a}^6+1.
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20) If x = a-b, y = b-c, z = c-a, then find the value of {x}^3+{y}^3 + {z}^3 -3xyz .
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Sum of Algebra
21) If x=y=333 and z = 334 then find the value of {x}^3+{y}^3+(z)^3-3xyz.
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22) {a}^2 + {b}^2 + {c}^2 = ab +bc + ca, then find the value of \frac{a+c}{b}
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23) If a+b+c = 4 then find the value of {a}^3 + {b}^3 + {c}^3 - 12{c}^2 +48c-64.
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24) 4x -5z = 16 and xz = 12 then find the value of 64{x}^3 - 125{z}^3.
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