wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If l, m, n are the sides of ΔLMN and
∣ ∣ ∣l2m2n2(l+12)(m+1)2(n+1)2(l1)2(m1)2(n1)2∣ ∣ ∣=0, then theΔLMN is an

A
Equilateral
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Isosceles
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Right angled
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B Isosceles
∣ ∣ ∣l2m2n2(l+1)2(m+1)2(n+1)2(l1)2(m1)2(n1)2∣ ∣ ∣=0
R2R2R3
∣ ∣ ∣l2m2n24l4m4n(l1)2(m1)2(n1)2∣ ∣ ∣=0
C1C1C2,C2C2C3
∣ ∣ ∣(lm)(l+m)(mn)(m+n)n2(lm)mnn(lm)(l+m)2(lm)(mn)(m+n)2(mn)(n1)2∣ ∣ ∣=0
(lm)(mn)∣ ∣ ∣(l+m)(m+n)n211n(l+m2)(m+n2)(n1)2∣ ∣ ∣=0
C1C1C2
(lm)(mn)∣ ∣ ∣(ln)(m+n)n201n(ln)(m+n2)(n1)2∣ ∣ ∣=0
R1R1R3
(lm)(mn)(ln)∣ ∣ ∣022n101n1(m+n2)(n1)2∣ ∣ ∣=0
(lm)(mn)(ln)=0
l=m or m=n or l=n
Hence, the triangle is isosceles

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