SarkariPYQ

SSC CGL 2024 PYQ — Question 66

SSC CGL - 23 Sep 2024 - Shift 1 • Quantitative Aptitude • Q66

Back to paper

Simplify

(232)3+(140)3+(353)3−3×232×140×353(232)2+(140)2+(353)2−2321×40−140×353−353×232{{(232)^3 + (140)^3 +(353)^3 -3 × 232 × 140 × 353} \over (232)^2+(140)^2+(353)^2 - 2321×40 - 140×353 - 353×232}. 

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 725.

(232)3+(140)3+(353)3−3×232×140×353(232)2+(140)2+(353)2−232×140−140×353−353×232\frac{(232)^3 + (140)^3 +(353)^3 -3 \times 232 \times 140 \times 353}{(232)^2+(140)^2+(353)^2 - 232\times140 - 140\times353 - 353\times232}

a3+b3+c3−3abc=(a+b+c)(a2+b2+c2−ab−bc−ca)a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)

a2+b2+c2−ab−bc−ca=(a+b+c)2−(ab+bc+ca)1a^2 + b^2 + c^2 - ab - bc - ca = \frac{(a + b + c)^2 - (ab + bc + ca)}{1}

⇒ 232 + 140 + 353 = 725

⇒ a + b + c = 725