If a=2+√3, then a+1/a=?
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33
GIVEn
If a=2+√3, then a+1/a=?
SOLUTIOn
- If a = 2 + √3
Then,
→ 1/a = 1/2 + √3
★ Rationalise its denominator
→ 1/a = 1/2 + √3 × 2 - √3/2 - √3
→ 1/a = 2 - √3/(2)² - (√3)²
→ 1/a = 2 - √3/4 - 3
→ 1/a = 2 - √3
So, the value of a + 1/a
- a = 2 + √3
- 1/a = 2 - √3
→ a + 1/a
→ 2 + √3 + 2 - √3
→ 4
Answered by
127
Using rationalisation,
Therefore,
=> 2 + 2
=> 4.
Hence, 4 is the required answer.
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