(18. Cor. 1.) (ax + b). (3 зах + 26 3 ax + 56 multiplying both sides of the equation by ax + 56), ах - 5b2 = 3ax + bax - 262; .. (17. Cor. 3.) bax = 362; (18. Cor. 2.) ✓ ax = 36; (19) squaring both sides, ax = 962, and (18. Cor. 2.) x = 962 a Since 3x - 1 = (√ 3x + 1) × (3x - 1); ... (18. Cor. 1.) √3x - 1 = 2; .. (17) by transposition, ✓ 3x = 2 + 1 = 3; .. (19) squaring both sides, 3x = 9, ах 41. Given ab = c + Vax-b, to find the value ax + b C Since ax = b2 = (√ ax + b). (√ ax — · b); b; b (17) by transposition, x + a = √ {a2 + x √ (b2 + x2)} ..(19) squaring both sides, x2 + 2 ax + a2 = a2 + x √ (b2 + x2) ; (17. Cor. 3:) x2 + 2 ax = x ✓ (b2 + x2) ; (18. Cor. 2.) x + 2a = √ (b2 + x2); and (19) squaring both sides, x2 + 4 a x + 4 a2 = b2 + x2 (17. Cor. 3.) 4αx + 4a2 = b2; (17) by transposition, 4 ax = b2 — 4a2; (18. Cor. 1.) 2 + x + √(2x + x2) = 4; .. (17) by transposition, ✓ (2x + x2) = 4 - 2 – x = 2 - X, and (19) squaring both sides, 2x + x2 = 4 - 4x + x2; (18. Cor. 1.) 5 + x + .. (17) by transposition, ☑ (5x + x2) = 15 - 5 - x = 10 and (19) squaring both sides, 5x + x2 = 100 X, 20x + x2; (5x + x2) = 15; and (19) squaring both sides, x = ..(17. Cor. 3.) + 2 = ax 4 and (18. Cor. 2.) -/- + 2 =✓ (à a 1 4 4 + (19.) squaring both sides. + + = ax a2 SECTION II. On the Solution of Simple Equations which involve more than one unknown Quantity. (23.) Ir the equation involve several unknown quantities, and definite values of these are required, there must necessarily be as many independent equations as there are unknown quantities. In which case, the values will be found by exterminating all the unknown quantities except one; and this may be done by either of the three following methods: 1. By equalizing the coefficients of the same unknown quantity in the several equations. 3. By equating different values of the same unknown quantity. 1. Of exterminating an unknown quantity by the first method in equations where two unknown quantities are concerned. If the coefficient of either unknown quantity in one equation be contained a certain number of times exactly in the coefficient of the same unknown quantity in the other, multiply the former equation by that number, then add it to, or subtract it from, the other equation, according as the signs are different or the same, and an equation arises, in which only one unknown quantity is found. |