Discussion
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- Question
- If a3 ? b3 = 56 and a ? b = 2, then the value of ( a2 + b2 ) is :
Options- A. ? 10
- B. ? 12
- C. 20
- D. 18
- Correct Answer
- 20
ExplanationAs we know from the algebra formula,
(a ? b)3 = a3 ? b 3 ? 3ab (a ? b) .......................(1)
As per given question,
a3 ? b 3 = 56 and a ? b = 2
Put these value in above equation (1) . We will get,
? 23 = 56 ? 3ab x 2
? 8 = 56 ? 3ab x 2
? 8 = 56 ? 6ab
? 6ab = 56 ? 8 = 48
? ab = 8 ...................... (i)
? a2 + b2 = (a ? b)2 + 2ab
? a2 + b2 = (a ? b)2 + 2ab
Put the value of
? a2 + b2 = 22 + 2 x 8
? a2 + b2 = 4 + 16 = 20 - 1.
If (5x2 ? 3y2) : xy = 11 : 2, then the positive value of x is : y
Options- A. 7 2
- B. 5 2
- C. 3 2
- D. 5 3 Discuss
- 2. If P = (0.08) 2, Q = 1/(0.08) 2 and R = (1 ? 0.08) 2 ? 1, then out of the following the true relation is
Options- A. Q < P and P = R
- B. P < Q and P = R
- C. Q < R < P
- D. R < P < Q Discuss
- 3. The sum of two numbers is 24 and their product is 143. The sum of their squares is
Options- A. 296
- B. 295
- C. 290
- D. 228 Discuss
- 4. The product of two alternate odd integers exceeds three times the smaller by 12. What is the larger integer?
Options- A. 9
- B. 7
- C. 3
- D. 5 Discuss
- 5. What is the solution of the equations x - y = 0.9 and 11(x + y) -1 = 2?
Options- A. x = 3.2, y = 2.3
- B. x = 1, y = 0.1
- C. x = 2, y = 1.1
- D. x = 1.2, y = 0.3 Discuss
- 6.
If x = 2 + ?3, then the value of ?x + 1 is : ?x
Options- A. ?3
- B. ?6
- C. 2 ?6
- D. 6 Discuss
- 7.
If 5a + 1 = 5, the value of 9a2 + 1 is 3a 25a2
Options- A. 34 5
- B. 39 5
- C. 42 5
- D. 52 5 Discuss
- 8. If a, b, c are real and
a3 + b3 + c3 = 3abc and
a + b + c ≠ 0 , then the relation between a, b, c will be
Options- A. a + b = c
- B. a + c = b
- C. a = b = c
- D. b + c = a Discuss
- 9. The line passing through the points (? 2, 8) and (5, 7)
Options- A. does not cut any axes
- B. cuts x- axis only
- C. cuts y - axis only
- D. cuts both the axes Discuss
- 10. If the difference of two numbers is 3 and the difference of their squares is 39; then the larger number is:
Options- A. 9
- B. 12
- C. 13
- D. 8 Discuss
Elementary Algebra problems
Search Results
Correct Answer: 3 2
Explanation:
Correct Answer: R < P < Q
Explanation:
Correct Answer: 290
Explanation:
Let the two numbers be P and Q.
According to given question,
Sum of two numbers = 24
? P + Q = 24 ...................... (1)
Product of two numbers = 143
and, PQ = 143 .......................... (2)
As we know the formula,
? P 2 + Q2 = (P + Q)2 ? 2PQ
Put the value from the equation (1) and (2), We will get
? P 2 + Q2 = (24)2 ? 2 × 143
? P 2 + Q2 = 576 ? 286 = 290
Correct Answer: 7
Explanation:
Let two alternate odd integers odd integers be (2x+1) and (2x+5).
Then according to the question,
(2x + 1) (2x + 5) = 3(2x + 1) + 12
? (2x + 1) (2x + 5 - 3) = 12
? 2x2 + 3x - 5 = 0
On solving this quadratic equation,we get
x = 1 and x = -5/2
x = -5/2 is not a integer ? x = 1
Then, larger integer = 2x + 5 = 2 x 1 + 5 = 7
Correct Answer: x = 3.2, y = 2.3
Explanation:
x - y = 0.9 ...(i)
and 11(x + y)-1=2
? 11/ (x + y) = 2
? 2(x + y) =11
? x + y = 11/2 ...(ii)
On solving Eqs.(i) and (ii),we get
x = 3.2
and y = 2.3
Correct Answer: ?6
Explanation:
Correct Answer: 39 5
Explanation:
Correct Answer: a = b = c
Explanation:
Given that :-
Now ,a3 + b3 + c3 = 3abc
( a+b+c )( a2 + b2 + c2 - ab - bc - ca ) + 3abc = 3abc
( a+b+c )( a2 + b2 + c2 - ab - bc - ca ) = 0
∴ a² + b² + c² - ab - bc - ca = 0 or a + b + c ≠ 0
Where ,
a = b = c
Correct Answer: cuts y - axis only
Explanation:
As indicated in the graph, the line passing through the points cuts Y-axis only.
Correct Answer: 8
Explanation:
Let the numbers are p and q.
p ? q = 3 ? (1)
p2 ? q2 = 39
(p ? q) (p + q) = 39 ? x + y = 13 ? (2)
Adding eqn (1) and (2)
p + q + p ? q = 16 ? p = 8
? q = 3
Hence, 8 is the larger number.
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