Algebra for elitmus

 Algebra for elitmus

Algebra for elitmus

The importance of algebra is high in elitmus you can expect around 2 questions from algebra.

Important formulae of algebra specific to elitmus.

1. a² – b² = (a – b)(a + b)

2. (a+b)² = a² + 2ab + b²

3. a² + b² = (a – b)² + 2ab

4. (a – b)² = a² – 2ab + b²

5. (a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc

6. (a – b – c)² = a² + b² + c² – 2ab – 2ac + 2bc

7. (a + b)³ = a³ + 3a² b + 3ab²  + b³ ; (a + b)³ = a³ + b³ + 3ab(a + b)

8. (a – b)³ = a³– b³  – 3ab (a - b)

9. a³ – b³ = (a – b)(a² + ab + b² )

10. a³ + b³ = (a + b)(a²  – ab + b² )

Important shortcuts of algebra specific to elitmus

1. if  (x+1/x) = a, then (x³+1/x³) = a³-3a and (x⁴+1/x⁴ )=a⁴-4a²+2

2. geometric mean of two number a and b is sqrt(ab)

3. arithmetic mean of two number a and b is (a+b)/2

4. if 1/a+1/b+1/c=1/(a+b+c) where (a+b+c)=0 then (a+b)(b+c)(c+a)=0

Sample questions with the solution of algebra specific to elitmus

1. The sum of a two digit number ‘n’ and the number obtained by interchanging digits of n is    99. The difference of the digits of ‘n’ is 3, with the tens place being larger than the units place. Find the number ‘n’.

Solution:

Let the number be ‘xy’, where x and y are single digits.

=> The number is 10x + y

=> Reverse of the number = yx = 10y + x

=> Sum = 11 x + 11 y = 11 (x + y) =99  (given)

=> x + y = 9

Also, we are given that the difference of the digits is 3 and x > y.

=> x – y = 3

Therefore, x = 6 and y = 3

Thus, the number is 63.

 

2. If x3 + y3 = 9 and x + y = 3, then the value of x4+y4 is,

solution:

squaring both side (x+y)³=3³

=>  x³+y³+3*x*y*(x+y)=27

=>  9*x*y= 27-9

=>  x*y=18/9

=>  xy=2

now, (x²+y²)²=x⁴+y⁴+2*x²*y²

=>  x⁴+y⁴ = (x²+y²)²- 2*(xy)²

=>  x⁴+y⁴ = ((x+y)² - 2*xy)² - 8

=>  x⁴+y⁴ = (9- 4)² - 8

=>  x⁴+y⁴ = 17

3. If x+1/2x = 2, find the value of 8x3+1/x3

Solution:

(a+b)³ = a³+b³+3*a*b(a+b)

=> x+1/2x =2

=> 2x+1/x =4

=> cube of both side 8x³+1/x³ + 3 * 2(4) = 64

=> 8x3+1/x3= 64-24 = 40

4. If 5√x +12√x =13√x then value of x is,
Solution:

always check with options like trial and error method for these type of question here value of x will be 4.

(5)²+(12)² = (13)² 

=> 25+144=169.

=> 169 = 169

5. If b2 + 1⁄b2 = 1, then value of b3 + 1⁄b3 is ,

Solution:

let (b+1/b) = c

=> b²+1/b²+2=c²

=> 1 = c² -2 

=> c² = 3 

=> c= sqroot(3)

=> (b+1/b)³ = c³

=> b³+ 1/b³ + 3sqroot(3) = 3sqroot(3)

=> b3 + 1⁄b3 = 0

Sample quiz with solution and score of algebra specific to elitmus