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Question

If a + b + c = 8 and ab + bc + ca = 11, then what is the value of a 3+ b 3+ c 3- 3abc?

This question was previously asked in
SSC Selection Post 2019 Graduation Level Question Paper (16 Oct, 2019) (Shift 3)
The correct answer is

248

The correct answer is 248.

Substitute all values into the main identity: (8)(42 - 11) . Perform the calculation: 8 \times 31 = 248 . Result The value of a^3 + b^3 + c^3 - 3abc is 248. These identities help in solving various problems involving polynomials and algebraic expressions efficiently.

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  2. If \(\rm \left(x^2+\frac{1}{x^2}\right)=18 \) and x > 1, what is the value of \(\rm \left(x^3-\frac{1}{x^3}\right)\)?

  3. If \(\sqrt 5 \) = 2.24, then find the value of \(\sqrt {\frac{{\sqrt {5 }-1 }}{{\sqrt {5 }+1 }}} \) .

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Important Questions from Identities

  1. If \(2x + { {1} \over 3x}= 5, x ≠ 0\) , then what is the value of  \(27x^3+{{1} \over 8x^3}\) ?

  2. If x 2 + 4y 2 = 40, xy = 6 and x > 2y then the value of x - 2y is:

  3. \(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)
  4. If a(a + b + c) 2= 1792; b(a + b + c) 2= 1536; c(a + b + c) 2= 768 then what will be the value of a?

  5. If a + b + c = 5, a 2+ b 2+ c 2= 27, a 3 + b 3 + c 3 = 125, then the value of  \(\frac{abc}{5}\)  is: 

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