8x3 - 125y3 का मान ज्ञात कीजिए यदि :
LO
(i) 2x - 5y = 18 और (ii) xy = 15 है।
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Finding values
Given: 2x - 5y = 18, xy = 15
To find: the value of 8x³ - 125y³
Solution:
We must know that,
- a³ - b³ = (a - b) (a² + b² + ab)
- a² + b² = (a - b)² + 2ab
Now, 8x³ - 125y³
= (2x)³ - (5y)³
= (2x - 5y) {(2x)² + (5y)² + 2x * 5y}
= (2x - 5y) {(2x - 5y)² + 2 * 2x * 5y + 2x * 5y}
= (2x - 5y) {(2x - 5y)² + 30 xy}
= 18 (18² + 30 * 15)
= 18 (324 + 450)
= 18 * 774
= 13932
Answer: 8x³ - 125y³ = 13932
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Given (1) 2x - 5y= 18 and (ii) xy = 15 then find the value of 8x3 - 125y3.7
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