Archive
21st of March 2017
Mathematics
Q:

1.The value of m if 2x^m + x^3 – 3x^2 – 26 leaves a remainder of 226 when it is divided by x – 2.

2. If A + B = 225°, then the value of (1 + tan A)(1 + tan B) is.

Sahil Kumar Sahoo - CBSE - Class X

Tuesday, March 21, 2017 at 17:53:PM

A:

Hi Sahil,

Please post 1 query per question since we have many queries lined up. However, I will still be helping you with both the queries since you may not have been aware.

First query:

begin mathsize 16px style straight x minus 2 space is space straight a space factor comma space
so space straight x equals 2 space has space to space satisfy space the space given space expression. space
Substitute space straight x equals 2 space in space the space given space equation.
2 times 2 to the power of straight m plus 2 cubed minus 3 times 2 squared minus 26 equals 226
rightwards double arrow 2 to the power of straight m plus 1 end exponent plus 2 cubed minus 3 times 2 squared minus 26 equals 226
rightwards double arrow 2 to the power of straight m plus 1 end exponent plus 8 minus 12 minus 26 equals 226
rightwards double arrow 2 to the power of straight m plus 1 end exponent equals 256
rightwards double arrow 2 to the power of straight m times 2 equals 256
rightwards double arrow 2 to the power of straight m equals 128
rightwards double arrow 2 to the power of straight m equals 2 to the power of 7
So comma space straight m equals 7
end style

Second query:

begin mathsize 16px style Given space straight A plus straight B equals 225
rightwards double arrow tan left parenthesis straight A plus straight B right parenthesis equals tan 225
rightwards double arrow fraction numerator tanA plus tanB over denominator 1 minus tanAtanB end fraction equals tan left parenthesis 180 plus 45 right parenthesis
rightwards double arrow fraction numerator tanA plus tanB over denominator 1 minus tanAtanB end fraction equals tan 45 equals 1
rightwards double arrow tanA plus tanB equals 1 minus tanAtanB
rightwards double arrow tanA plus tanB plus tanAtanB equals 1 space... left parenthesis asterisk times right parenthesis
Consider comma space
left parenthesis 1 plus tanA left parenthesis 1 plus tanB right parenthesis
equals 1 plus tanB plus tanA plus tanAtanB
equals 1 plus 1... left parenthesis from space asterisk times right parenthesis
equals 2 end style

Tuesday, March 21, 2017 at 18:37:PM