Selection Post Phase XIV (Graduate)17 Sep 2026Shift 1Algebra

If 8x3 − 27y3 = (2x − 3y)(Mx2 + Ny2 + Oxy), find M2 + N2 + O2.

यदि 8x3 − 27y3 = (2x − 3y)(Mx2 + Ny2 + Oxy) है, तो M2 + N2 + O2 ज्ञात कीजिए।

Answer और ExplanationAnswer and explanation

Answer: (C) 133

8x3 − 27y3 = (2x)3 − (3y)3
A3 − B3 = (A − B)(A2 + AB + B2), जहाँ A = 2x, B = 3y
= (2x − 3y)(4x2 + 9y2 + 6xy)
इसलिए M = 4, N = 9, O = 6
M2 + N2 + O2 = 16 + 81 + 36 = 133
✓
उत्तर 133 है।
8x3 − 27y3 = (2x)3 − (3y)3
A3 − B3 = (A − B)(A2 + AB + B2) with A = 2x, B = 3y
= (2x − 3y)(4x2 + 9y2 + 6xy)
So M = 4, N = 9, O = 6
M2 + N2 + O2 = 16 + 81 + 36 = 133
✓
The answer is 133.

Source: Selection Post Phase XIV (Graduate) · 17 Sep 2026 · Shift 1। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (Graduate) · 17 Sep 2026 · Shift 1. Solution by Prashant Sir, from Vijayastra.