If the sum of squares of two real numbers is 41 and their

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If the sum of squares of two real numbers is 41 and their sum is 9, then the sum of cubes of these two numbers is

1. 169
2. 209
3. 189
4. 198

Correct Option: C

Let the two real numbers be x and y.
According to the question,
x² + y² = 41
x + y = 9
∴ (x + y)² = x² + y² + 2xy
⇒ 81 = 41 + 2xy
⇒ 2xy = 81 – 41 = 40

⇒ xy =	40	= 20
	2

∴ x³ + y³ = (x + y)³ – 3xy (x + y)
= (9)³ – 3 × 20 (9)
= 729 – 540 = 189