Quadratic inequations (1 Viewer)

kpad5991 · Apr 18, 2017

what range of values may x^2 +3 take if a) 2 < x < 4
b) x is greater than -1 and less than and equal to 3

1729 · Apr 18, 2017

kpad5991 said:
what range of values may x^2 +3 take if a) 2 < x < 4
b) x is greater than -1 and less than and equal to 3

$\noindent If $2 < x < 4$ then $4 < x^2 < 16$ and thus $7 < x^2 + 3 < 19$

$\noindent If $-1 < x \leq 3$ then $0 \leq x^2 \leq 9$ and thus $3 \leq x^2 + 3 \leq 12$

KingOfActing · Apr 19, 2017

1729 said:
$\noindent If $2 < x < 4$ then $4 < x^2 < 16$ and thus $7 < x^2 + 3 < 19$

$\noindent If $-1 < x \leq 3$ then $1 < x^2 \leq 9$ and thus $4 < x^2 + 3 \leq 12$

Your second one isn't correct, take for example 0 (which is in the range (-1, 3] ). 0^2 + 3 = 3 < 4

The correct solution would be:

$-1 < x \leq 3 \\\iff -1 < x \wedge x \leq 3 \\\iff 0 \leq x^2 \wedge x^2 \leq 9 \\\iff 3 \leq x^2 + 3 \leq 12$

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Quadratic inequations (1 Viewer)

kpad5991

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KingOfActing

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