mathematics - linear equations in two variables

Class 9 - Mathematics

Linear Equations in Two Variables

MCQ
Q&A
Question:
If x = 2 + 3 , find the value of x2 + 1 x2
Answer:

We have, x = 2 + 3

โˆด 1 x = 1 2 + 3 = 1 2 + 3 2 - 3 2 - 3 = 2 - 3 22 - ( 3 )2 = 2 - 3 4 - 3 = 2 - 3

Now, x2 + 1 x2 = x + 1 x 2 = 2

=> x2 + 1 x2 = 2 + 3 + 2 โˆ’ 3 2 โˆ’ 2 = 42 โˆ’ 2 = 16 โˆ’ 2 = 14

ALITER we have, x = 2 + 3

โˆด 1 x = 1 2 + 3 = 1 2 + 3 2 - 3 2 - 3 = 2 - 3 22 - ( 3 )2 = 2 - 3 4 - 3 = 2 - 3

Thus, x2 + 1 x2 = 2 + 3 2 + 2 โˆ’ 3 2

=> x2 + 1 x2 = 22 + (3)2 + 2 ร— 2 3 + 22 + (3)2 โˆ’ 2 ร— 2 3

=> x2 + 1 x2 = 4 + 3 + 4 3 + 4 + 3 โˆ’ 4 3 = 14

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Questions and Answers


Linear Equations in Two Variables - Questions
1. If both a and b are rational numbers, find the values of a and b in each of the following equalities :

(i) 3 โˆ’ 1 3 + 1 = a + b 3 (ii) 3 + 7 3 โˆ’ 7 = a + b 7 (iii) 5 + 2 3 7 + 4 3 = a + b 3

(iv) 5 + 3 7 โˆ’ 4 3 = 47 a + 3 b (v) 5 + 3 5 โˆ’ 3 = a + b 15 (vi) 2 + 3 3 2 โˆ’ 2 3 = a โˆ’ b 6

Answer
2. Rationalise the denominator in each of the following:

(i) 2 7 [NCERT] (ii) 2 3 3 (iii) 2 7 11
Answer
3.

Rationalise the denominator of : 1 7 + 3 2


Answer
4. Prove that :

= 1 3 โˆ’ 8 โˆ’ 1 8 โˆ’ 7 + 1 7 โˆ’ 6 โˆ’ 1 6 โˆ’ 5 + 1 5 โˆ’ 2 = 5
Answer
5. If x = 1 โˆ’ 2 , find the value of x โˆ’ 1 x 3
Answer
6. If x = 3 - 2 2 , find the value of x2 + 1 x2
Answer
7. Simplify:
(i) 5 + 2 2 [NCERT] (ii) 11 - 5 2
Answer
8. Simply each of the following: (i) 5 16 5 2 (ii) 4 243 4 3
Answer
9.

Rationalise the denominator of :
2 3

10. Simply the following expression:
(i) 3 + 3 2 + 2 [NCERT] (ii) 5 + 7 2 + 5
Answer
11.

If 2 = 1.414 , find the value of 3 รท 6 upto three places of decimals.


Answer
12. Evaluate 15 10 + 20 + 40 - 5 - 80 , is being given that 5 = 2.236 and 10 = 3.162
Answer
13. if x = 3 + 2 3 โˆ’ 2 and y = 3 โˆ’ 2 3 + 2 , find x2 + y2


Answer
14. Given that 5 = 2.236 approximately, find to three places of decimals the value of 2 5
Answer
15. Prove that :

1 1 + 2 + 1 2 + 3 + 1 3 + 4 + 1 4 + 5 + 1 5 + 6 + 1 6 + 7 + 1 7 + 8 + 1 8 + 9 = 2
Answer
16. Simplify each of the following :

(i) 3 5 โˆ’ 3 + 2 5 + 3 (ii) 4 + 5 4 โˆ’ 5 + 4 โˆ’ 5 4 + 5 (iii) 5 โˆ’ 2 5 + 2 โˆ’ 5 + 2 5 โˆ’ 2
Answer
17. if a = 2 โˆ’ 5 2 + 5 and b = 2 + 5 2 โˆ’ 5 , find a2 โˆ’ b2
Answer
18. Simplify:
(i) 5 + 5 5 - 5 (ii) 3 + 2 2 3 - 2 2
Answer
19. Find the value to three places of decimals, of each of the following: It is given that 2 = 1.414 , 3 = 1.732, 10 = 3.162 and 5 = 2.236 (approx.)

(i) 1 2 (ii) 1 3 (iii) 1 10


Answer
20. if x = 1 2 โˆ’ 3 , find the value of x 3 โˆ’ 2x2 โˆ’ 7x + 5
Answer
21. Simplify each of the following by rationalising the denominator:

(i) 1 5 + 2 (ii) 5 + 6 5 - 6 (iii) 7 + 3 5 7 - 3 5 (iv) 2 3 โˆ’ 5 2 3 + 3 3
Answer
22. If x = 2 + 3 , find the value of x2 + 1 x2
Answer
23.

Find the value to three places of decimals, of each of the following:
It is given that 2 = 1.414 , 3 = 1.732, 10 = 3.162 and 5 = 2.236 (approx.).
(i) 2 + 1 5 (ii) 2 - 3 3 (iii) 10 - 5 2


Answer
24. Simplify each of the following by rationalising the denominator:

(i) 1 5 + 2 (ii) 5 + 6 5 - 6 (iii) 7 + 3 5 7 - 3 5 (iv) 2 3 โˆ’ 5 2 3 + 3 3
Answer
25.

Rationalise the denominator of : 1 3 + 2


Answer
26.

Rationalise the denominator of : 5 3 - 5


Answer
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