Equation exercises-5

shariful Gurukul

13 years ago

Today is our topic of discussion Equation exercises-5 .

Equation exercises-5

Use formula to solve the following equations:

Solve:

Solve :

1. (2x+3)(y-1) = 14, (x − 3) (y2) = – 1

2. (x-2)(y-1) = 3, (x+2) (2y-5) = 15

3. x²=7x+6y, y² = 7y+6x =

4. x²=3x+2y, y² = 3y+2x

5. x+4/y=1, y + = y+4/x=25

6. y+3= 4/x, x-4=5/3y

7. xy-x²=1, y² – xy=2

8. x²-xy= 14, y²+ xy = 60

9. x²+y²=25, xy= 12

10. x+y/x-y +x-y /x+y=10/3 x² – y² = 3

11. x²+ xy + y² = 3, x² – xy + y² = 7

12. 2x²+3xy + y² = 20, 5x²+4y² = 41

1. The sum of the areas of two square regions is 481 square metres; if the area of the rectangle formed by the two sides of the two squares is 240 square metres, what are the lengths of a side of each of the squares?

2. The sum of the squares of two positive numbers is 250; the product of the numbers is 117; find the two numbers.

3. The length of a diagonal of a rectangle is 10 metres. The area of a rectangle whose sides are the sum and difference of the sides of the former one is 28 square metres. Find the length and breadth of the former rectangle.

4. The sum of squares of two numbers is 181 and the product of the numbers is 90. Find the difference of the squares of the two numbers.

5. The area enclosed by a rectangle is 24 square metres. The length and breadth of another rectangle are respectively 4 metres and 1 metre more than the length and breadth of the first rectangle and the area enclosed by the later rectangle is 50 square metres. Find the length and breadth of the first rectangle.

6. Twice the breadth of a rectangle is 23 metres more than its length. If the area enclosed by the rectangle is 600 square metres, find the length and breadth of the rectangle.

7. The perimeter of a rectangle is 8 metres more than the sum of its diagonals. If the area enclosed by the rectangle is 48 square metres; find its length and breadth.

8. If a number of two digits be divided by the product of its digits, the quotient is 2. When 27 is added to the number, the digits in the number change their places. Find the number.

9. The perimeter of a rectangular garden is 56 metres and one diagonal is 20 metres. What is the length of the side of the square which encloses an area equal to the area of that garden?

10. The area of a rectangular field is 300 square metres and its semi-perimeter is 10 metres more than a diagonal. Find the length and breadth of the rectangular field.

Solve:

1. 2^x + 3^y = 31

2^x – 3^y = – 23

2. 3 ^ x = 9 ^ y

5^(x + y + 1) =25^(xy)

3. 3^x.9^y = 81

2x-y = 8

4. 2^ x. 3^y = 18

2^(2x) .3 ^ y = 36

5. a^x. a^(y + 1) = a^7

a^ (2y) .a^(3x + 5) = a^20

6. y²x²= x

x^(2x) =y^4 (y ≠1)

7. y ^ x = 4 y ^ 2 = 2 ^ x

8. 4 ^ x = 2 ^ y (27) ^ (xy) = 9 ^ (y + 1)

9. 8y ^ x – y ^ (2x) = 16 2 ^ x = y ^ 2

Solve:

1. What is the value of b in equation ax² + bx + c = 0 while comparing with the equation x²- x – 12 = 0?

1) 0

2) 1

3) -1

4) 3

2. Which one is the solution of the equation 16^x= 4*+1?

1) 2
2) 1
3) 4
4) 3

3. A root of the equation x²- x – 13 = 0 is:

4. A root of the system of equations y ^ x = 9, y ^ 2 = 3 ^ x :

According to the information given below answer questions 5 and 6.
The difference of the squares of two positive whole numbers is 11 and the product of the numbers is 30.

5. What are the numbers?
1) 1 and 30
2) 2 and 15
3) 5 and 6
4) 5 and -6

6. What is the sum of the squares of the numbers?

1) 1
2) 5
3) 61
4) sqrt(41)

7. The sum of a number and its multiplicative inverse is 6. The formation of equation is

(i) x + 1/x = 6
(ii) x ^ 2 + 1 = 6x
(iii) x ^ 2 – 6x – 1 = 0

Which one is true?

1) i and ii
2) i and iii
3) ii and iii
4) i, ii and iii

8. Which one is the solution of 2 ^ (px – 1) = 2 ^ (2px – 2)

1) p/2
2) p
3) – p/2
4) 1/p

9. Solve the following equations graphically: