Definition 1: Perfect squares are numbers or expressions that are the product of a
number or expression multiplied to itself (7 times 7 is 49, so 49 is a
perfect square).
Definition 2: <span>Binomials are algrebraic expressions containing only two terms.</span><span />
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Definition 3: Trinomials are algebraic expressions that contain three terms. </span><span />
Perfect square trinomials are algebraic expressions with three terms that are created by multiplying a binomial to itself. There are two formulas for perfect square trinomials:
.
From these formulas you can see that:
A. <span>"Neither of the perfect squares can have a minus sign" is true statement;
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B. "<span>The first and third terms must be perfect squares" is true statement;
</span>
C. "<span>If the perfect square terms are
and
then the other term must be
" is false statement;
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D. "<span>None of the above is a property of a perfect square trinomial" is consequently false statement.
</span>
Option B:
Both n and m must be rational.
Solution:
Given information:
Sum of two numbers, n and m are rational.
<u>To find which statements are true:</u>
Option A: Both n and m may be rational but do not have to be.
It is not true because n and m given is rational.
It have to be rational.
Option B: Both n and m must be rational.
Yes, n and m must be rational then only the sum of numbers are rational.
It is true.
Option C: Both n and m must be irrational.
Sum of irrationals will be sometimes irrational and sometimes can't add.
So it is not true.
Option D: One number is rational and the other is irrational.
Rational and irrational cannot be add.
So it is not true.
Option B is true.
Both n and m must be rational.
Answer:
x = 4, y = 4 or you can say (4, 4)