If p=106, q=105 and r=104, then the value of p
2
+q
2
+r
2
−pq−qr−rp is:
- A0
- B2
- C1
- D3
Solution & Step-by-step Explanation
We use the well-known algebraic identity:
p
2
+q
2
+r
2
−pq−qr−rp=
2
1
[(p−q)
2
+(q−r)
2
+(r−p)
2
]
Given:
p=106
q=105
r=104
Calculate the differences:
p−q=106−105=1
q−r=105−104=1
r−p=104−106=−2
Substitute these differences back into the identity formula:
Value=
2
1
[(1)
2
+(1)
2
+(−2)
2
]
Value=
2
1
[1+1+4]
Value=
2
1
×6=3
p
2
+q
2
+r
2
−pq−qr−rp=
2
1
[(p−q)
2
+(q−r)
2
+(r−p)
2
]
Given:
p=106
q=105
r=104
Calculate the differences:
p−q=106−105=1
q−r=105−104=1
r−p=104−106=−2
Substitute these differences back into the identity formula:
Value=
2
1
[(1)
2
+(1)
2
+(−2)
2
]
Value=
2
1
[1+1+4]
Value=
2
1
×6=3