b²
Solve one of the formulas for A, then substitute that into the other formula to solve for B, then substitute the solution for B into one of the formulas to solve for A. Here is how: Givens: A+B=8 A-B=9 So: If A+B=8 then A=8-B Next, substitute this into the other formula... A-B=9 (8-B)-B=9 (-B) - B = 1 (-2B) = 1 B= (- 1/2) Next, substitute the solution for B into one of the formulas to solve for A.... A+B=8 A+ (-1/2) = 8 A = 8 and 1/2 So... B= (- 1/2) A = 8 and 1/2
-1
B x A = BA
That factors to (a + 1)(a + b) a = -1, -b b = -a
b = 14
one a/b X b/a = a/a X b/b =1/1 = 1
OK, so first let's translate it into math notation: 5/(2b)*2 = (b-1)/2 Now note that the 2 of 2b and the multiplication by 2 cancel out in the left side, giving 5/b = (b-1)/2 To get rid of the fractions, multiply both sides by 2b, giving: 5*2 = b*(b-1) simplify [b^2 = b*b is a notation for b squared] b^2 - b - 10 = 0 This is a second degree equation. Without using formulas to solve it, notice that each expression of the form b^2 + a*b = (b + a/2)^2 - (a^2)/4 this is called splitting off the square. In our case we get (b - 1/2)^2 - 1/4 - 10 = 0 or (b - 1/2)^2 = 1/4 + 10 hence (b - 1/2) = +- (41/4)^(1/2) = +- (1/2)*41^(1/2) 41^(1/2) is a notation for the square root of 41.
0.6667
Solve one of the formulas for A, then substitute that into the other formula to solve for B, then substitute the solution for B into one of the formulas to solve for A. Here is how: Givens: A+B=8 A-B=9 So: If A+B=8 then A=8-B Next, substitute this into the other formula... A-B=9 (8-B)-B=9 (-B) - B = 1 (-2B) = 1 B= (- 1/2) Next, substitute the solution for B into one of the formulas to solve for A.... A+B=8 A+ (-1/2) = 8 A = 8 and 1/2 So... B= (- 1/2) A = 8 and 1/2
-1
B x A = BA
That factors to (a + 1)(a + b) a = -1, -b b = -a
-83
0.3333
b = 14
2 is
yes -a=-b means you multiplied each side by -1 which is allowed