Clearing this Equation of fractions, by multiplying each numerator into the denominator of the other fraction, 24x-6x-18-24x-2/6x-12. Transposing, and uniting similar terms, Multiplying both terms of the fraction by √x+c+√x−c, (243...2) COMPLETE EQUATIONS In which the Unknown Quantity is contained in a 32. Find the value of x in the Equation 6+√√3x+4=11. Transposing, and uniting similar terms, √3x+4=5. Squaring both sides, 3x+4=25; whence x=7. 33. Find the value of x in the Equation 24-9x2215. Transposing, and uniting similar terms, 2x2+9=-9. Squaring both sides, 2x2+9=81; whence x=±6. 34. Find the value of x in the Equation 20-√x3+40=4. Transposing, and uniting similar terms, √x3+40=-16. Squaring both sides, x3+40=256. Transposing, and uniting similar terms, 3216; whence x= -6. Then, since this Equation has three roots (255), the other two roots will be found by reducing it to a quadratic by division, (253). Dividing both sides of the Equation 23-216-0 by x-6, we have x2+6x+36=0, or from which we shall find x= −3+√−27, or −3—√√—27. 32x3+16x2x+16x3+64x2. Dividing both sides of this Equation by x2, we have 32x+16=x2+16x+64; from which we shall find x= = 12, or 4. Rationalizing the denominator (243...2), we have Extracting the square root of each side of this Equation, Rationalizing the denominator (243...2), we shall have Extracting the square root of each side of this Equation, x2-16-144-72x+9x2; from which we shall find x=5, or 4. 42. Find the value of x in the Equation, 3√x3+37×(x3-37)3 =64. This Equation may be put under the form (x3+37)3×(x3+37)* =64 Multiplying together the two binomials in the first member (x3+37)=64, (241...3). From this Equation we shall have which will give x=3. x3=27; The other two values of x (255), will be found by reducing the cubic Equation to a quadratic, (253). Dividing both sides of the Equation x3-27-0 by x-3, from which we shall find x=-3-3. Equations of a Quadratic Form with reference to a Power or Root of the Unknown Quantity. 43. Find the value of x in the Equation 24-2x2+6=230. |