Solve the following equation: 3t^3 = 192t a) 0 b) -8 c) 8, -8 d) 0, 8, -8 Simpli
ID: 3037483 • Letter: S
Question
Solve the following equation: 3t^3 = 192t a) 0 b) -8 c) 8, -8 d) 0, 8, -8 Simplify x + 1/x + 3 + x - 3/x - 1 a) 2(x^2 - 5)/(x + 3)(x - 1) b) 2x^2 + 9/(x + 3)(x - 1) c) 2(x^2 + 5)/(x + 3)(x - 1) d) 2x^2 + 10/(x + 3)(x - 1) Simplify x^2 - 16/4x - x^2 x^2 + 4x/x^2 a) -1 b) 1 c) 4 - x d) x - 4 Solve: 2/x + 2 + 1/x - 2 = 4/x^2 - 4 a) 2 b) -2 c) 3 d) no solution Simplify (6x^2 y^3 z^4)^3/2 a) 6x^3 y^4 z^6 Squareroot 6y b) x^3 y^4 z^6 Squareroot 6y c) 6x^3 y^4 z^6 Squareroot y d) none of these Rationalize and simplify Squareroot 2 + Squareroot 3/Squareroot 2 - Squareroot 3 a) 5 + 2 Squareroot 6 b) -5 -2 Squareroot 6 c) 5 - 2 Squareroot 6 d) none of the above Solve: Squareroot 8v + 40 = v + 5 a) -5 b) 3 c) -3 d) -5, 3 Simplify 3 + 3i/2 + 2i a) 12 + 12i b) 12 c) 3/2 Solve #9-10 by any method. x^2 + 6x = -40 a) 4, -10 b) -4, 10 c) -3 plusminus i Squareroot 31 6x^3 + 10x^2 = 4x a) 0, 1/3, -2 b) 0, -1/3, 2 c) 2, 1/3, -2Explanation / Answer
3t3=192t or 3t3-192t = 0 or, 3t(t2-64)= 0 or, 3t(t-8)(t+8)= 0 so that either t = 0 or, t = 8 or, t = -8 Option (d) is the correct answer (x+1)/(x+3) +(x-3)/(x-1) =[ (x+1)(x-1)+(x-3)(x+3)]/(x+3)(x-1)= (x2-1 +x2-9)/ (x+3)(x-1)=(2x2-10)/ (x+3)(x-1)== 2(x2 -5)/ (x+3)(x-1).Option (a) is the correct answer. [(x2-16)/(4x-x2)]/[ (x+4x)/x2] = [(x+4)(x-4)/x(4-x)]* [x2/x(x+4)] = [-(x+4)/(x+4)]* (x2/x2)= -1. Option (a) is the correct answer. 2/(x+2) +1/(x-2) = 4/(x2-4) or, [2(x-2)+1(x+2)]/(x+2)(x-2)= 4/(x2-4) or, (3x-2)/( x2-4) =4/(x2-4) Now, if x2 -4 is not 0 i.e. if x is not 2 or, -2, then on multiplying both the sides by x2-4, we get 3x-2 = 4 or, 3x = 2+4= 6 so that x = 6/3 = 2. However, while arriving at this answer, we had assumed that x is not equal to 2 or -2. Hence, there is no solution.Option (d) is the right answer. (6x2y3 z4)3/2 = 63/2x2*3/2y3*3/2 z4*3/2 =63/2x3y9/2z6 = 6x3y4z6(6y). Option (a) is the correct answer. [(2+3)/ (2-3)] =[(2+3)(2+3)/ (2-3)(2+3)] = (2+26+3)/(2-3) = -5-26. Option (b) is the correct answer. (8v+40) = v+5 so that 8v+40 = (v+5)2 or, 8v +40 = v2 +10v +25 or, v2+2v -15 = 0 or, v2+5v-3v -15= 0 or, v(v+5)-3(v+5) = 0 or, (v+5)(v-3) = 0 so that either v = -5 or, v =3. Option (d) is the correct answer. (3+3i)/(2+2i) = (3+3i)(2-2i)/(2+2i)(2-2i) = (6-6i2)/(4-4i2) =(6+6)/(4+4) = 12/8 = 3/2. Option (c ) is the correct answer. x2+6x = -40 or, x2+6x +40 = 0 . On using the quadratic formula, x = [ -6± {62-4*1*40}]/2*1 = [-6± (36-160)]/2 = [-6± ( -124)]/2 = -3± (-31) = -3± i31. Option (c ) is the correct answer. 6x3+10x2= 4x or, 6x3+10x2- 4x= 0 or, 2x(3x2+5x -2) = 0. Hence either x = 0 or, 3x2+5x -2= 0, in which case 3x2+6x-x -2= 0 or, 3x(x+2)-1(x+2) = 0 or, (3x-1)(x+2) = 0. Thus, in this case, either x = 1/3 or, x = -2. Option (a) is the correct answer.