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Question: Answered & Verified by Expert
If x,y,zR, x+y+z=5, x2+y2+z2=9, then length of interval in which x lies is
MathematicsQuadratic EquationBITSATBITSAT 2019
Options:
  • A 8/3
  • B 4/3
  • C 2/3
  • D 1/3
Solution:
2440 Upvotes Verified Answer
The correct answer is: 4/3

We have,

x+y+z=5

x2+y2+z2=9

 x2+y2+(5-x-y)2=9

 y2+x2-5x-5y+xy+8=0

 y2+y(x-5)+x2-5x+8=0

Since yR

(x-5)2-4x2-5x+80

 x2-10x+25-4x2+20x-320

 3x2-10x+70

 3x2-7x-3x+70

 (3x-7)(x-1)0

 x1,73
Length of interval =73-1=43

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