Dear Aspirants,
We know that some of you are keen on knowing the algebric formulae for SSC CGL 2018 Examination. So, in the list below we have mentioned nearly 75% of all the Algebric formulae:
1. (a + b)2 = a2 + 2ab + b2; a2 + b2 = (a + b)2 − 2ab
2. (a − b)2 = a2 − 2ab + b2; a2 + b2 = (a − b)2 + 2ab
3. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
4. (a + b)3 = a3 + b3 + 3ab(a + b); a3 + b3 = (a + b)3 − 3ab(a + b)
5. (a − b)3 = a3 − b3 − 3ab(a − b); a3 − b3 = (a − b)3 + 3ab(a − b)
6. a2 − b2 = (a + b)(a − b)
7. a3 − b3 = (a − b)(a2 + ab + b2)
8. a3 + b3 = (a + b)(a2 − ab + b2)
9. an − bn = (a − b)(an−1 + an−2b + an−3b2 + ··· + bn−1)
10. an = a.a.a . . . n times
11. am.an = am+n
13. (am)n = amn = (an)m
14. (ab)n = an.bn
15. a0 = 1 where a ∈ R, a 6= 0
18. ap/q = √q ap
19. If am = an and a 6= ±1, a 6= 0 then m = n
20. If an = bn where n 6= 0, then a = ±b
21. If √x, √y are quadratic surds and if a + √x = √y, then a = 0 and x = y
22. If √x, √y are quadratic surds and if a+ √x = b+ √y then a = b and x = y
29. if a + ib = 0 where i = √−1, then a = b = 0
30. if a + ib = x + iy, where i = √−1, then a = x and b = y
32. The roots are real and distinct if ∆ > 0.
33. The roots are real and coincident if ∆ = 0.
34. The roots are non-real if ∆ < 0.
35. If α and β are the roots of the equation ax2 + bx + c = 0, a 6= 0 then
i) α + β = −b
a = − coeff. of x
coeff. of x2
ii) α · β = c
a = constant term
coeff. of x2
36. The quadratic equation whose roots are α and β is (x − α)(x − β)=0
i.e. x2 − (α + β)x + αβ = 0
i.e. x2 − Sx + P = 0 where S =Sum of the roots and P =Product of the
roots.
We hope that all the above formulae will help you to a great extent in appearing for the examination in SSC CGL Examination 2018.
All the Best!!
Avision
Howrah, Liluah & Kolkata
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