| Mathematics - 1836 - 798 pages
...arranged according to the powers of any letter in it, and if, in that form, the second term is equal to **twice the product of the square roots of the first and third terms,** then that trinominal is the square of a binominal formed by connecting the roots of the first andthird... | |
| Horatio Nelson Robinson - Algebra - 1844 - 186 pages
...preceive 1st. That it consists of three terms. 2d. Two of these terms, the first and last are squares. 3d. **The middle term is twice the product of the square roots of the first and** last. Now let us suppose that a2 is lost, and we have only x2-\-2a&'. We know these terms cannot make... | |
| James Thomson - 1844 - 328 pages
...62 = 4Ğe. This is evident from § 151. ; for we saw there, that when a trinomial is a square, its **middle term is twice the product of the square roots of the first and third.** Hence, that ax* i-bx+c may be a square, we must have to=2o5c% ; and from this, by dividing by x, and... | |
| James Thomson - Algebra - 1845 - 316 pages
...if 62 = 4ac. This is evident from § 151. ; for we saw there, that when a trinomial is a square, its **middle term is twice the product of the square roots of the first and third.** Hence, that ax2 + bx + c may be a square, we must have bx=i2.a*eix ; and from this, by dividing by... | |
| Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...1st. That it consists of three terms; 2d. Two of its terms, the first and the third, are squares; 3d. **The middle term is twice the product of the square roots of the first and** last term. Now let us suppose the third term, a3, to be lost, and we have only xa-|-2ax. We know these... | |
| Charles William Hackley - Algebra - 1846 - 544 pages
...• 9aĞ— 48a<62+64asi< is a perfect square ; for the two extreme terms are perfect squares, and **the middle term is twice the product of the square roots of the** extreme terms; hence the square root of the trinomial is Or, . Sa^—Sab*. An expression such as 4a!+... | |
| Horatio Nelson Robinson - Algebra - 1848 - 354 pages
...1st. That it consists of three terms; 2d. Two of its terms, the first and the third, are squares; 3d. **The middle term is twice the product of the square roots of the first and** last term. Now let us suppose the third term, a2, to be lost, and we have only x*-\-2ax. We know-these... | |
| Joseph Ray - Algebra - 1848 - 252 pages
...trinomial can be separated into two binomial factors, when the extremes are squares and positive, and **the middle term is twice the product of the square roots of the** extremes. See Articles 79 and 80. Thus: a'+2ab+b*=(a+b)(a+b). a'—2ab+b'=(a—b)(a—b). 2d. Any binomial,... | |
| Horatio Nelson Robinson - Algebra - 1850 - 358 pages
...consists of three terms; 2d. Two of its terms, the first and the third, are squares; 3d. The middle tern **is twice the product of the square roots of the first and** Isfst term. Now let us suppose the third term, a 2 , to be lost, and we have only x2-\-2ax. We know... | |
| Joseph Ray - Algebra - 1848 - 250 pages
...trinomial can be separated into two binomial factors. when the extremes are squares and positive, and **the middle term is twice the product of the square roots of the** extremes. Seğ Articles 79 and 80. Thus: o*+2ab+^=(a+b)(a+b). a2— 2a6+6*=(a— b)(a— 6). 2d. Any... | |
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