Question
Download Solution PDFयदि a = 3 + 2√2, तो (a6 – a4 – a2 + 1)/a3 का मान ज्ञात कीजिए
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
a = 3 + 2√2
प्रयुक्त अवधारणा:
a2 – b2 = (a – b)(a + b)
a3 + b3 = (a + b)3 – 3ab(a + b)
गणना:
a = 3 + 2√2
1/a = 1/(3 + 2√2)
⇒ 1/a = (3 – 2√2)/{(3 + 2√2) × (3 – 2√2)}
⇒ 1/a = (3 – 2√2)/{32 – (2√2)2}
⇒ 1/a = (3 – 2√2)/(9 – 8)
⇒ 1/a = (3 – 2√2)
अब,
a + 1/a = 3 + 2√2 + 3 – 2√2
⇒ a + 1/a = 6
(a6 – a4 – a2 + 1)/a3
⇒ a3 – a – 1/a + 1/a3
⇒ (a3 + 1/a3) – (a + 1/a)
⇒ {(a + 1/a)3 – 3(a + 1/a)} – (a + 1/a)
⇒ (63 – 3 × 6) – 6
⇒ 216 – 18 – 6
⇒ 192
∴ (a6 – a4 – a2 + 1)/a3 का अभीष्ट मान 192 है
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