Math, asked by kamalpapers1, 2 months ago

solve the inequality

 \sqrt{x + 3}  <   \sqrt{7 - x}
Plz solve it solution is required urgently

urgent solutions will be appreciated and will be marked as brainliast..​

Answers

Answered by TheBrainlistUser
3

\large\underline\mathfrak\red{Correct \:  Question \:  :- }

\sf{x - 1 < \sqrt{7 - x}  } \\

\large\underline\mathfrak\red{Solution  \: :- }

\sf\implies{7 - x \geqslant 0} \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\ \sf\implies{ x - 7 \leqslant 0} \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\ \sf\implies{x€( - ∞7)} \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\ \sf\implies{squaring \: both \: sides} \\

\sf\implies{x {}^{2} - 2x + 1 < 7 - x } \\ \sf\implies{x {}^{2} - x - 6 < 0 } \:  \:  \:  \:  \:  \:  \:  \:  \:  \\ \sf\implies{(x - 3)(x + 2) < 0} \:  \\ \sf\implies{x€( - 2 \: and \: 3)} \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:

Answer : x€(-2,3)

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