If p & q are distinct reals, then 2[(x−p)(x−q)+(p−x)(p−q)+(q−x)(q−p)]=(p−q)2+(x−p)2+(x−q)2 is satisfied for
A
no value of x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
exactly one value of x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
exactly two values of x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
infinite values of x
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is D infinite values of x LHS = 2[(x−p)(x−q)+(p−x)(p−q)+(q−x)(q−p)] = 2(x2−xq−px+pq+p2−pq−px+qx+q2−pq−qx+px) = 2(x2+p2+q2−px−qx−pq) = (2x2+2p2+2q2−2px−2qx−2pq) RHS = (p−q)2+(x−p)2+(x−q)2 = p2+q2−2pq+x2+p2−2px+x2+q2−2qx = (2x2+2p2+2q2−2px−2qx−2pq) = LHS Since LHS=RHS,therefore all values of x satisfy the equation ⇒x∈R Hence,(D) is the correct choice.