What is (4(a-2))^2-4(a^2)>0 ?

The solution to (4(a-2))^2-4(a^2)>0 is a 4

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(4(a-2))^2-4(a^2)>0

(4 (a - 2))^{2} - 4 (a^{2}) > 0

a < \frac{4}{3} or a > 4

Interval Notation

(- \infty, \frac{4}{3}) \cup (4, \infty)

Decimal Notation

a < 1.33333 \dots or a > 4

Solution steps

(4 (a - 2))^{2} - 4 a^{2} > 0

Rewrite in standard form

3 a^{2} - 16 a + 16 > 0

Factor

3 a^{2} - 16 a + 16 : (3 a - 4) (a - 4)

(3 a - 4) (a - 4) > 0

Identify the intervals

a < \frac{4}{3} or a > 4

\frac{x + 1}{2} > \frac{1}{x + 2}

(n - 3)^{2} - (n + 4) (n - 4) < 43

12 x^{2} + x - 6 < 0

\frac{( 5 x - 8 )}{( x - 3 )} \geq 3

5 x - 3 x^{2} > 0

What is (4(a-2))^2-4(a^2)>0 ?
The solution to (4(a-2))^2-4(a^2)>0 is a< 4/3 \lor a>4