Practice Questions

സംഖ്യ= X ആയാൽ 

സംഖ്യയുടെ വ്യുൽക്രമം = 1/X

X + 1/X = 6

X² + 1 = 6X

X² - 6X + 1 = 0

X = 3 + 2√2

6 @ 3 = 6/3 + 6

= 2 + 6 = 8

2 @ 1 = 2/1 + 2 = 4

6@3 - 2@1 = 8 - 4 = 4

6#5 = 30 + 6 - 5 = 31

3 # 2 = 6 + 3 - 2 = 7

(6#5)× (3#2) = 31 × 7 = 217

5#4 = 20 + 5 + 4 = 29

1 # 2 = 2 + 1 + 3 = 5

5#4 - 1#2 = 29 - 5 = 24

a+b = 8, ab= 12

(a - b)² = (a + b)² - 4ab

=64 - 48

= 16

a - b = √16

= 4

a+b = 8, ab= 12

(a- b)² = (a +b)² - 4ab

= 64 - 48

=16

a+b =10, ab= 32

(a + b)² = a² + b² + 2ab 

⇒ a² + b² = (a + b)² - 2ab 

 = 10² - 2 × 32

 = 100 - 64

= 36

a+b =12, ab= 22

a² + b² = (a+b)² - 2ab

  = 12² - 2× 22

 = 144 - 44

 = 100

$2^m-2^{m-1}-4=0 \implies2^m-2^{m-1}=4$$2^{m-1}(2-1)=4\implies2^{m-1}=2^2$$m-1=2\implies{m=3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

$(2^x)(2^y)=2^{x+y}=8=2^3\implies{x+y}=3....(1)$
$9^x\times3^y=3^{2x+y}=81=3^4\implies{2x+y}=4....(2)$
$(2)-(1)\implies{x}=1,y=2$
&nbsp;

8a - b²=24.......(1) , 8b + b² = 56 ......(2)

(1) + (2)

8(a + b) = 80

a + b = 80/8 = 10

(b – c)(b + c) + (c – a)(c + a) + (a – b) (a + b) 

= b² - c² + c² - a² + a² - b²

= 0

5x²+ -7x² + 13x² + 11x²+ -5x² 

= (5 -7 +13 + 11 -5)x²

= 17x²

(3x - 6)/x - (4y -6)/y + (6z + 6)/z = 0

3 - 6/x - 4 + 6/y + 6 + 6/z = 0

6/x - 6/y - 6/z = 5

1/x - 1/y - 1/z = 5/6

(x + y)² + (x - y)² 

= x² + 2xy +y² + x² - 2xy + y²

= 2(x² + y²) 

(x+ y)² = 2(x² + y²)  - (x - y)² 

= 2 × 10 - 16

  = 20 - 16

 = 4

( x + y) = 2

x-y=5 ,

 x²-y²= 55

→ (x+y)(x-y)=55

(x+y) × 5 = 55

x+y = 11

y = {(x+y) - (x-y)}/2
 
 = {11-5}/2

 = 6/2

=3

$(a+b)(a-b)$
$=a\times a-a\times b+b\times a-b\times b$
$ = a^2 -ab +ab - b^2$
$ = a^2 - b^2$

സംഖ്യകൾ X,  Y ആയാൽ

X+Y = 6

XY = 8

1/X + 1/Y = X+Y/XY

= 6/8

= 3/4

(a)² - (b)² = (a + b)(a - b)

(203 + 107)² - (203 - 107)² = (310)² - (96)²


(310)² - (96)² = (310 + 96)(310 - 96) 

= (406)(214) 

= 86884

$\frac{4-10}{5}=\frac{k-20}{10}$
$-6/5=(k-20)/10$
$-12=k-2 0\implies{k}=8$

നാലാമത്തെ സംഖ്യ X ആയാൽ

-125 + 965 + -367 + X = 0

X + 473 = 0

X = -473

സംഖ്യ X ആയാൽ 

(3X-5)/2 = 8

3X - 5 = 16

3X = 21

X = 7

x + 1 = 23

x = 23 - 1 = 22

3x + 1=( 3 × 22) + 1

 = 66 + 1

 = 67

സംഖ്യ x എന്ന് എടുത്താൽ ,

4x - 5 = 3x +3

 x = 8

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