...that is a Perfect Square. By Arts. 85 and 86 a trinomial is a perfect square when its first and last terms are perfect squares and positive, and the middle...term is twice the product of the square roots of the end terms. The sign of the middle term determines whether the square root of the trinomial is a sum...

...trinomial is a perfect square if its first and last terms are perfect squares and positive, and its middle term is twice the product of the square roots of the first and last terms. Thus, 16 a2 — 24 а6 + 9 62 is a perfect square. The rule for extracting the square root...

...trinomial is a perfect square if its first and last terms are perfect squares and positive, and its middle term is twice the product of the square roots of the first and last terms. Thus, 16 a2 — 24 ab + 9 62 is a perfect square. The rule for extracting the square root...

...62= ±(a + 6). When an expression can be arranged in three terms of the form a2 + 2a6 + V (in which the middle term is twice the product of the square roots of the other two), the square root can be written down at once. Ex. 2. Ex. 3. x2 + Sx + 16 = (x + 4)2. In...

...considered. 80. When a Trinomial is a Perfect Square. A trinomial is a perfect square if the first and last terms are perfect squares and positive, and the middle...twice the product of the square roots of the first and last terms (§ 61, p. 28). Thus, 16 a2 — 24 ab + 9 b2 is a perfect square. To extract the square...

...adding and also subtracting 9 x2«2. For the trinomial to be a perfect square, its middle term must be twice the product of the square roots of the first and third terms, according to Prop. .4. 3 i2a2 = 12 х*а3 — 0 x'2a3. What is twice the product of the square roots...

...example, let it be required to solve the equation x' + 3z r= 4 We have seen that in any trinomial square, the middle term is twice the product of the square roots of the first and third terms ; hence the square root of the third term is equal to the second term divided by twice the square root...

...square. In each product The first term is a perfect square, j The last term is a perfect square. J "' ' ' The middle term is twice the product of the square roots of the square terms. The sign of the middle term is + or - according as the sign of the second term of the...

...(42/-6z)2. 9. (fe-H)2. 2. (a-4)2. 6. (3ac-46)2. 10. (v-l2w)2 3. (c + 9)2. 7. (x+4)2. 11. (4 o + 13 b)2. Note that in each of these trinomial squares, the...term which will form a perfect trinomial square : 13. x2+4a^ 15. c2 + 16. 17. 62-46. 14. a2 + 9. 16. x2+l2x. 18. s2 + 4. Can you substitute other numbers...

...factors, that is, if it is a perfect square. By the binomial theorem it will be a perfect square if the middle term is twice the product of the square roots of the first and last terms (like a2 + 2 ab + b2). Hence (3) will have two equal values of x (that is, equal roots)...