...-r> ' en"-g' J g—cn 6. When neither of the above rules will apply, if the formula can be resolved into two parts, one of which is a square, and the other the product of any two «impie factors, the irrationality of it may be destnoyed^by putting V(a + ex .+ car) = </{(d...

...place of the former, we shall have 2tt(ra3 -ama)~ 6. When the formula, last mentioned, can be separated into two parts, one of which is a square, and the other the product of two factors, its solution may be obtained by putting the sum of the square and the product so formed, equal to the...

...we shall have _ams(b-5)-n2(b+8) 2a(?i2— am8) 6. When the formula, last mentioned, can be separated into two parts, one of which is a square, and the other the product of two factors, its solution may be obtained by putting the sum of the square and the product so formed, equal to the...

...value of x as will render rational the expression 6x — 2. CASE 6. When the proposed expression can be divided into two parts, one of which is a square, and the other the product of two factors. This is the last case in which any general method of proceeding can be pointed out, and may often be...

...3X25—2X36 75 — 72 3 , CASE 6. When neither of the foregoing will apply, if the formula can be resolved into two parts, one of which is a square, and the other the product of any two simple factors. Put V(a+bx+eaf) = y\(d+exY + (f+gx) (h+kx)\ = n(f+gx} ; in which case we shall...

...x as will render rational the expression V8x2 + 6x — 2. CASE 6. When the proposed expression can be divided into two parts, one of which is a square, and the other the product of two factors. This is the last case in which any general method of proceeding can be pointed out, and may often be...

...fa and therefore * 7--5 — «-«• hs — fr hrf — fnf CASE VI. When the proposed expression can be divided into two parts, one of which is a square, and the other the product of tut factors. This is the last case in which any general method of proceeding can be pointed out, and...

...itself. Ans. When u = 1, the first = , and the second = . CASK VI. When mx* + nx+p can be separated into two parts, one of which is a square, and the other the product of two simple factors, that is, when ^ (mxll + nx + p) — kx)}. Assume J{(ax+e)* + (f+gx) (h+kx)} = {(ax+e)+u...

...-^f, oí &c. 234. It sometimes happens that an expression of the form ax* + bx + c may be separated into two parts, one of which is a square, and the other the product of two factors, so that we will hare ax> + bx + с = (mx + n)3 + (px +f)(qx + g). In such cases the value of x may...

...=-, 61 &c. 234. It sometimes happens that an expression of the form ax1 + bx + с may be separated into two parts, one of which is a square, and the other the product of two factors, so that we will have аз? + bx + c = (mx + n)" + (px +f)(qx + g) . In such cases the value of x may...