Prove that 2 divides a if and only if 2 divides ao. Prove that 4 divides a if and only if 4 divides ao + 2a1. Prove that 8 divides a if and only if 8 divides ao + 2a1 + 4a2.

Q: 2 and B= 1 0. then Show that if A = 6. -1 2 (A + B)(A + B) # A² + 2AB + B?

A: Given that A=-1201 and B=10-12 We have to show that A+BA+B≠A2+2AB+B2

Q: Select two positive integers a and b with 5 <  a  ≤  20  and 5  <  b ≤  20.

A:

Q: 8. Let a, b and c be any positive real numbers. Prove that b² + c² a²+b² 2c a² + c² + 2b 2a > a+b+c.

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Q: a.Given an integer a, then a² + 4a + 5 is odd if and only if a is even. b. There exists a positive…

A: Since you have posted multiple subpart questions, we will solve the first three questions for you.…

Q: verify that 3(A + B) = 3A + 3B

A:

Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              =&gt; k(15 - 13) = 2k for any integer k              =&gt; 15 k -…

Q: Show that if 9 | a3 + b3 + c3 then 3 divides at least one of the integers a, b, or c.

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Q: how that Q(√2 + √3) =Q(√2,√3).

A:

Q: Find the product AB if [2 5 A = 3 9. -21 6 4 and B = -1 6. 1 17 8. -3] 7 8. 2

A: We find the product AB  by using matrix product.

Q: Prove (2b +1 , 7b + 3)=1

A:

Q: Indicate the least integer n for which (3x⁰+2x²)(x³ +3x) x+14x € 0(x¹).

A: Given: 3x6+2x2x3+3xx4+14x∈Oxn To find: Least integer n for which the given condition holds.

Q: it is a less than 1 not a bigger than one

A: Here a is less than 1.

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.