Proof by contradiction

Show thatk² – 4k + 5 is positive for all real values of k.

A student was asked to prove by contradiction that “There are no positive integers x and y such that 3x 2y2x 5y 28 ”

The start of the student’s proof is shown below.

Show the calculations and statements needed to complete the proof.

A student attempts to answer the following question: Given that x is an obtuse angle, use algebra to prove by contradiction that

The student starts the proof with: Assume that sinx – cosx < 1 when x is an obtuse angle

The start of the student’s proof is reprinted below. Complete the proof.

Assume that sinx – cosx < 1 when x is an obtuse angle

Use proof by exhaustion to show that for n ₃ , n_n≤ 4

Given that m³ + 5 is odd, use proof by contradiction to show, using algebra, that m is even.

Use proof by exhaustion to show that for n ₃ , n_n≤ 4

Given that m³ + 5 is odd, use proof by contradiction to show, using algebra, that m is even.

Prove by contradiction that there are no positive integers p and q such that