X2 + y2 = 100 = r2 r = 10
x2 + x2 = 2x2
y varies inversely as x2 so y = c/x2 for some constant c. When x = 5, y = 4 So c = x2y = 100 that is y = 100/x2 Then, when x = 2, y = 100/4 = 25
x2 + 20x - 39 = 0: Add 61 giving: x2 + 20x + 100 = (x + 10)2
x4+100=29x2 x4+100-29x2=0 (X2)2+100-29x2=0 (x2-25)(x2-4)=0 (x+5)(x-5)(x+2)(x-2) x=-5 x=5 x=-2 x=2
x2 − 36y2
If: y = x2+20x+100 and x2-20x+100 Then: x2+20x+100 = x2-20x+100 So: 40x = 0 => x = 0 When x = 0 then y = 100 Therefore point of intersection: (0, 100)
X2 + y2 = 100 = r2 r = 10
a dot
x2 + x2 = 2x2
x2 = 18y2/5 + 10 Or if you want to isolate x: x = ± √(18y2/5 + 10)
If 2x2 + 10 = 100 then: 2x2 = 100 -10 2x2 = 90 x2 = 90/2 x2 = 45 x = 6.708 (to 3 decimal places only)
y varies inversely as x2 so y = c/x2 for some constant c. When x = 5, y = 4 So c = x2y = 100 that is y = 100/x2 Then, when x = 2, y = 100/4 = 25
x2 + 20x - 39 = 0: Add 61 giving: x2 + 20x + 100 = (x + 10)2
x2 + 20x +0 =30 [(20/2)2 =100] x2 + 20x + 100 =30 +100 √(x+10)2=√130 x+10=√130 x= −10+√130 √ means square root
There is no integer solution. Quadratic formula gives x = -17.66 or 5.66
x1:y1 = x2:y2 4:-2 = x2:5 x2 = (4*5)/-2 x2 = -10