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Question : 110 of 150
Marks:
+1,
-0
Solution:
Given,
x2=|| sin‌θ | cos‌θ | 0 |
| −cos‌θ | sin‌θ | 1 |
| sin‌θ | cos‌θ | 2 |
| On expanding
x2=|| sin‌θ | cos‌θ | 0 |
| −cos‌θ | sin‌θ | 1 |
| sin‌θ | cos‌θ | 2 |
| along
C3 , we get
x2=0−1|| sin‌θ | cos‌θ |
| sin‌θ | cos‌θ |
| +2|| sin‌θ | cos‌θ |
| −cos‌θ | sin‌θ |
| =−1(sin‌θ‌cos‌θ−sin‌θ‌cos‌θ)+2(sin2θ+cos2θ) =−1×0+2×1 ⇒
x2=2⇒x=±√2 If
x=√2, then
4x2+x‌sin‌+5=4×(√2)2 −√2+5 =8−√2+5=(13−√2) If
x=−√2, then
4x2+x‌sin‌+5 =4×(−√2)2+√2+5 =8+√2+5=(13+√2)
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