a= √3+√2 হলে, a3 +3a+3a-1+a-3 এর মান কত?
Solution
Correct Answer: Option D
দেওয়া আছে,
a = √3 + √2
1/a = 1/(√3 + √2)
= 1(√3 - √2)/(√3 + √2)(√3 - √2)
= (√3 - √2)/(√3)2 - (√2)2
= (√3 - √2)/(3 - 2)
= (√3 - √2)
a + 1/a = √3 + √2 + √3 - √2 = 2√3
প্রদত্ত রাশি = a3 + 3a + 3a- 1 + a- 3
= a3 + 1/a3 + 3a + 3/a
= (a + 1/a)3 - 3.a.(1/a)(a + 1/a) + 3(a + 1/a)
=( 2√3)3 - 0
= 8 × 3√3
= 24√3
a = √3 + √2
1/a = 1/(√3 + √2)
= 1(√3 - √2)/(√3 + √2)(√3 - √2)
= (√3 - √2)/(√3)2 - (√2)2
= (√3 - √2)/(3 - 2)
= (√3 - √2)
a + 1/a = √3 + √2 + √3 - √2 = 2√3
প্রদত্ত রাশি = a3 + 3a + 3a- 1 + a- 3
= a3 + 1/a3 + 3a + 3/a
= (a + 1/a)3 - 3.a.(1/a)(a + 1/a) + 3(a + 1/a)
=( 2√3)3 - 0
= 8 × 3√3
= 24√3
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