If x = √7 + √3, then find the exact value of x2 + 16x2.
यदि x = √7 + √3 है, तो x2 + 16x2 का सटीक मान ज्ञात कीजिए।
Answer और ExplanationAnswer and explanation
Answer: (B) 20
x2 = 7 + 3 + 2√21 = 10 + 2√21
16x2 = 1610 + 2√21 × 10 − 2√2110 − 2√21 = 16(10 − 2√21)100 − 84 = 10 − 2√21
x2 + 16x2 = 10 + 2√21 + 10 − 2√21 = 20
✓
उत्तर 20 है।
x2 = 7 + 3 + 2√21 = 10 + 2√21
16x2 = 1610 + 2√21 × 10 − 2√2110 − 2√21 = 16(10 − 2√21)100 − 84 = 10 − 2√21
x2 + 16x2 = 10 + 2√21 + 10 − 2√21 = 20
✓
The answer is 20.
SMART APPROACH
दोनों भाग x और 4x का गुणनफल (Product) 4 है। 4x = 4√7 + √3 = √7 − √3 (क्योंकि 7 − 3 = 4)। इसलिए x + 4x = 2√7 और x2 + 16x2 = (2√7)2 − 2 × 4 = 28 − 8 = 20।
The two parts x and 4x have product 4. 4x = 4√7 + √3 = √7 − √3 (because 7 − 3 = 4). So x + 4x = 2√7 and x2 + 16x2 = (2√7)2 − 2 × 4 = 28 − 8 = 20.
Source: Selection Post Phase XIV (12th) · 25 Sep 2026 · Shift 2। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (12th) · 25 Sep 2026 · Shift 2. Solution by Prashant Sir, from Vijayastra.