Consider this expression:
[tex]\[ \left|m^2 - 7\right| + n^2 \][/tex]

When [tex]\( m = -2 \)[/tex] and [tex]\( n = 5 \)[/tex], the value of the expression is [tex]\(\square\)[/tex].



Answer :

To find the value of the expression [tex]\(\left|m^2 - 7\right| + n^2\)[/tex] when [tex]\(m = -2\)[/tex] and [tex]\(n = 5\)[/tex], follow these steps:

1. Calculate [tex]\(m^2\)[/tex]:
[tex]\[ m = -2 \implies m^2 = (-2)^2 = 4 \][/tex]

2. Calculate [tex]\(|m^2 - 7|\)[/tex]:
[tex]\[ m^2 = 4 \implies m^2 - 7 = 4 - 7 = -3 \][/tex]
Taking the absolute value:
[tex]\[ |m^2 - 7| = |-3| = 3 \][/tex]

3. Calculate [tex]\(n^2\)[/tex]:
[tex]\[ n = 5 \implies n^2 = 5^2 = 25 \][/tex]

4. Add the results of the absolute value and [tex]\(n^2\)[/tex]:
[tex]\[ \left|m^2 - 7\right| + n^2 = 3 + 25 = 28 \][/tex]

Therefore, the value of the expression [tex]\(\left|m^2 - 7\right| + n^2\)[/tex] when [tex]\(m = -2\)[/tex] and [tex]\(n = 5\)[/tex] is [tex]\(28\)[/tex].