wiz-icon
MyQuestionIcon
MyQuestionIcon
4
You visited us 4 times! Enjoying our articles? Unlock Full Access!
Question

Let ABC be a triangle such that ACB=π6 and let a, b and c denote the lengths of the sides opposite to A, B and C respectively. The value(s) of x for which a=x2+x+1, b=x21 and c=2x+1 is (are)

A
(2+3)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1+3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
2+3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
43
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 1+3
Using cosine rule for C

cosC=a2+b2c22ab
32=(x2+x+1)2+(x21)2(2x+1)22(x2+x+1)(x21)=(2x4+2x33x22x+1)2(x2+x+1)(x21)=(2x2+2x1)(x21)2(x2+x+1)(x21)
3=2x2+2x1x2+x+1
(32)x2+(32)x+(3+1)=0
x=(23)±32(32)
x=(2+3) , 1+3x=1+3 as (x>0).

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon