The Number Of Solution Of √(3x^2+6x+7) + √(5x^2+10x+14) = 4 - 2x

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SolveGuidesJoin / LoginUse appLogin0You visited us 0 times! Enjoying our articles? Unlock Full Access!Standard XIIMathematicsQuestionThe number of solution of √3x2+6x+7+√5x2+10x+14=4−2x−x2 is
  1. 1
  2. 4
  3. 2
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As √3x2+6x+7=√3(x+1)2+4≥2,and √5x2+10x+14=√5(x+1)2+9≥3∴L.H.S.≥5 and always positiveNow R.H.S.=4−2x−x2=5−(x+1)2≤5∴ The equation holds only when, L.H.S.=R.H.S.=5i.e.4−2x−x2=5⇒x2+2x+1=0⇒x=−1Hence, only one solution to the above equation.

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