...positive, and the second term plus (or minus) twice the product of their square roots (§ 96). Then, the square root of the third term is equal to the...term divided by twice the square root of the first. Hence, the square root of the expression which must be 3 x 3 added to ж2 + 3 x to make it a perfect...

...positive, and the second term plus (or minus) twice the product of their square roots (§ 96). Then, the square root of the third term is equal to the...term divided by twice the square root of the first. Hence, the square root of the expression which must be о ~ о added to я? + 3 x to make it a perfect...

...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...

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

...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 of the first and third terms? What must be added to 3 z2a2? What else must be done ? Why ? (4 x* + 12 zsas + 9 a4) - 9 A;2 = (2 *"...

...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...second term divided by twice the square root of the fimt. Therefore the square root of the quantity which must be Зx 3 added to x' -\- 3x to " complete...

...positive, and its second term plus or minus twice the product of their square roots (§ 167). Then, the square root of the third term is equal to the...term divided by twice the square root of the first. Hence, the square root of the expression which must be added to¿ + px to make it a perfect square,...