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**jacs** Prove by Mathematical Induction that $\displaystyle n^2-11n+30 \geq 0$ for $\displaystyle n\geq1$.

Step 1: Prove true for n = 1

$\displaystyle 1^2-11(1)+30=20$

hence true for n = 1

Step 2: Assume true for n = k

$\displaystyle k^2-11k+30 \geq 0$

Step 3: Prove true for n = k + 1

$\displaystyle (k+1)^2-11(k+1)+30 \geq 0$

LHS = $\displaystyle k^2+2k+1-11k-11+30$

not really sure what to do from here, tried this approach

$\displaystyle k^2-11k+30+2k-10$

since from step 2 we know that $\displaystyle k^2-11k+30 \geq 0$, but not sure if this is right as I do not know what to do with the 2k - 10

any insight appreciated