Question
Download Solution PDFनिम्नलिखित में से कौन-सा कथन सही है?
I.यदि x = 12, y = -2 और z = -10 है, तो x3 + y3 + z3 = 360 है।
II. यदि x + y = 48 और 4xy = 128 है, तो 4x2 + 4y2 = 4480 है।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
I. यदि x = 12, y = -2 और z = -10 है, तो x3 + y3 + z3 = 360 है।
II. यदि x + y = 48 और 4xy = 128 है, तो 4x2 + 4y2 = 4480 है।
प्रयुक्त अवधारणा:
a2 + b2 + 2ab = (a + b)2
गणना:
I. x3 + y3 + z3
⇒ (12)3 + (-2)3 + (-10)3
⇒ 1728 - 8 - 1000
⇒ 720
II. यहाँ, 4xy = 128
⇒ 2xy = 64 ....(1)
x + y = 48
⇒ (x + y)2 = 482
⇒ x2 + y2 + 2xy = 2304
⇒ x2 + y2 = 2304 - 64 (समीकरण 1 से)
⇒ x2 + y2 = 2240
⇒ 4x2 + 4y2 = 4 × 2240
⇒ 4x2 + 4y2 = 8960
इसलिए, न तो I और न ही II अनुसरण करता है।
∴ न तो I और न ही II सही है।
Last updated on Jul 7, 2025
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