How close to 0 do we need to take x so that(x^{2}+6x+9)<9.001?

shadsiei 2021-05-02 Answered

How close to 0 do we need to take x so that
(x2+6x+9)<9.001?

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Expert Answer

Clara Reese
Answered 2021-05-03 Author has 120 answers

Consider expression,
x2+6x+9
 x2+6(3x+3x)+9
(x2+3x)+(3x+9)
 x(x+3)+3(x+3)
(x+3)2
Hence the inequality will be,
(x+3)2<9.001
 x+33<9.001
 x+3<±3.00016666
Case(i): x+3< +3.00016666
 x<0.00016666
Case(ii): x+3<3.00016666
 x< 6.00016666
Since we need the solution which is close to zero,
The solution that satisfies should be
x<0.00016666
And it can be close to zero by 4 decimals(4 negative powers of 10)

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