Pleaseh help me with these question. I am having trouble understanding what to doPlease show all workThank you 2. For this question, you will prove that the roots of z² + 6x + 8.5 are irrational. In other words, thatVa € R, z² + 6x + 8.5=0=zQ.You may use, without proof, the quadratic formula. In other words, you may use the fact that for allreal a, b, and c,-b-√b²-4ac,-b+√b²-4acVr € R, (ar²+bx+c=0) ^ (b²-4ac > 0) ⇒ (z =-) V (x=2a2aPlease write complete proofs in each subquestion, without referring back to earlier subquestions.1(a)Prove that VI ER, re Q⇒ (r+1) EQ. Hint: go back to the definition of Q, and showthat if a satisfies that definition, then so does (x + 1).(b)Prove that Vr € R, z Q⇒ (x + 1) #Q. Hint: can you prove the contrapositive of thisstatement?(c)Prove that Vr € R, z² + 6x +8.5 = 0⇒xQ. Hint: you may want to use results thatare similar to 2a and 2b.

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(a) Prove that Vr € R, ze Q⇒ (x + 1) E Q. Hint: go back to the definition of Q, and show that if a satisfies that definition, then so does (x + 1). (b) Prove that Vr € R, z Q⇒ (x + 1) # Q. Hint: can you prove the contrapositive of this (c) statement? Prove that Vr € R, z² + 6x +8.5 = 0⇒zQ. Hint: you may want to use results that are similar to 2a and 2b. C