Vac-ad-bc + √bd by √√c - √d. 14. Divide acad 15. Divide ax+b*x+a+ y2+by х Ans. ab. by x+y. 16. Divide xy by √xy. Ans. √√y. 17. Divide 4 xy +4√ab-xy√ab-ab by 4-ab 20. Expand (√— √√√b)a. Ans. a2-4ab+6 ab−4a3¿a + b2. 21. Expand (4 — √√3)3. 22. Expand (a-— x−1)8. Ans. 10051/3. Ans. a-3 a1x1 + 3 ax2-2-8 27. Find the fourth root of 16a -32 ay3 +24 a* y* 8a+ y2+ys. Ans. 2 at — y3 SECTION XVIII. PURE EQUATIONS WHICH REQUIRE IN THEIR REDUCTION EITHER INVOLUTION OR EVOLUTION. 164. A PURE EQUATION is one that contains but one power of the unknown quantity; as, √x+ac=b, 4x2+3= 7, or 14 x" a b. 165. A PURE QUADRATIC EQUATION is one that contains only the second power of the unknown quantity; as, 6 x2 14a 51 b, a y2 = 13 cd, or a c z2 = 14. 166. RADICAL EQUATIONS, i. e. equations containing the unknown quantity under the radical sign, require Involution in their reduction Hence, to reduce radical equations, we deduce from these examples the following general RULE. Transpose the terms so that a radical part shall stand by itself; then involve each member of the equation to a power of the same name as the root; if the unknown quantity is still under the radical sign, transpose and involve as before; finally reduce as usual. x 12. Reduce — 30+ √x + 21 = √√x — 19. 168. Equations containing the unknown quantity involved to any power require Evolution in their reduction. 169. To reduce pure equations containing the unknown quantity involved to any power. Reduce the equation so as to have as one member the unknown quantity involved to any degree, and then extract that root of each member which is of the same name as the power of the unknown quantity. |