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- Question
- If x = 1 + ?2 + ?3, then the value of ( 2x4 ? 8x3 ? 5x2 + 26x ? 28) is
Options- A. 6 ?6
- B. 0
- C. 3 ?6
- D. 2 ?6
- Correct Answer
- 6 ?6
ExplanationGiven in the question ,
x - 1 = ?2 + ?3
On squaring both sides ,
x 2 ? 2x + 1 = 2 + 3 + 2?6
? x 2 - 2x - 4 = 2 ?6
On squaring again,
? x4 + 4x2 + 16 ? 4x3 ? 8x2 + 16x = 24
? x4 ? 4x3 ? 4x2 + 16x ? 8 = 0
? 2x4 ? 8x3 ? 8x2 + 32x ? 16 = 0
? 2x4 ? 8x3 ? 5x2 + 26x ? 28 ? 3x2 + 6x + 12 = 0
? 2x4 ? 8x3 ? 5x2 + 26x ? 28 = 3x2 ? 6x ? 12
? 2x4 ? 8x3 ? 5x2 + 26x ? 28 = 3 (x2 ? 2x ? 4)
? 2x4 ? 8x3 ? 5x2 + 26x ? 28 = 3 x 2?6 = 6 ?6 - 1. Area of the trapezium formed by x-axis; y-axis and the lines 3x + 4y = 12 and 6x + 8y = 60 is:
Options- A. 37.5 sq. unit
- B. 31.5 sq. unit
- C. 48 sq. unit
- D. 36.5 sq. unit Discuss
- 2.
If a = ? 3 - ? 2 , b = ? 3 + ? 2 , then the value of ?3 + ?2 ?3 - ?2 a 2 + b 2 is : b a
Options- A. 900
- B. 970
- C. 1030
- D. 930 Discuss
- 3. In the xy?coordinate system, if ( a, b) and ( a + 3, b + k) are two points on the line defined by the equation x = 3y ? 7, then k =?
Options- A. 7 3
- B. 1
- C. 9
- D. 3 Discuss
- 4. In xy?plane, P and Q are two points having co? ordinates (2, 0) and (5, 4) respectively. Then the numerical value of the area of the circle with radius PQ is
Options- A. 16 ?
- B. 32 ?
- C. 14 ?
- D. 25 ? Discuss
- 5. If ax + by = 6, bx ? ay = 2 and x 2 + y 2 = 4, then the value of ( a 2 + b 2) would be :
Options- A. 10
- B. 2
- C. 4
- D. 5 Discuss
- 6. If 4x = 18y, then the value of ( x/y - 1) is
Options- A. 1 3
- B. 7 2
- C. 2 3
- D. 3 2 Discuss
- 7. If a2 + b2 + c2 = 2 (a b c) 3 then the value of 2a 3b + 4c is
Options- A. 3
- B. 1
- C. 2
- D. 4 Discuss
- 8.
If x = 2 + ?3, y = 2 - ?3, then the value of x 2 + y 2 is x3 + y3
Options- A. 7 38
- B. 7 40
- C. 7 19
- D. 7 26 Discuss
- 9.
If 2x - 1 = 6, then the value of x2 + 1 is 2x 16x2
Options- A. 19 2
- B. 17 2
- C. 18 2
- D. 15 2 Discuss
- 10.
If x = 4ab , then the value of x + 2a + x + 2b is a + b x - 2a x - 2b
Options- A. a
- B. b
- C. 0
- D. 2 Discuss
Elementary Algebra problems
Search Results
Correct Answer: 31.5 sq. unit
Explanation:
Correct Answer: 970
Explanation:
Correct Answer: 1
Explanation:
Given in the question,
Points (a, b) and [(a + 3), (b + k)] will satisfy the equation x ? 3y + 7 = 0.
Points (a, b) in the equation x ? 3y + 7 = 0, We will get
? a ? 3b + 7 = 0 ...................... (i)
Points (a + 3), (b + k) in the equation x ? 3y + 7 = 0, We will get
a + 3 ? 3 (b + k) + 7 = 0
? a + 3 ? 3b ? 3 k + 7 = 0 (Rearrange the equation)
? a ? 3b + 7 + 3 ? 3 k = 0 (a ? 3b + 7 = 0 , Put the value from Equation (1) ), We will get
? 0 + 3 ? 3k = 0
? 3k = 3
? k = 1
Correct Answer: 25 ?
Explanation:
According to question ,
PQ = ?( 5 - 2 )2 + ( 4 - 0 )2
PQ = ?9 + 16 = 5
? Area of circle = ?r2
Area of circle = 25 ? sq. units
Correct Answer: 10
Explanation:
As we know that given in question,
ax + by = 6 ........................ (i)
bx ? ay = 2 ........................ (ii)
On squaring the both equation and adding,
a2 x2 + b2 y2 + 2abxy + b2 x2 + a2 y2 ? 2abxy = 36 + 4
? x2 (a2 + b2) + y2 (a2 + b2) = 40
? (a2 + b2) (x2 + y2) = 40
As per given question, x2 + y2 = 40 , Put this value in above equation, we will get
? (a2 + b2) Χ 4 = 40
? a2 + b2 = 10
Correct Answer: 7 2
Correct Answer: 1
Explanation:
As per the given question , we have
a2 + b2 + c2 = 2 (a b c) 3
⇒ a2 + b2 + c2 = 2a + 2b + 2c + 3 = 0
⇒ a2 2a + 1 + b2 + 2b + 1 + c2 + 2c + 1 = 0
⇒ (a 1)2 + (b + 1)2 + (c + 1)2 = 0
[If x2 + y2 + z2 = 0 ⇒ x = 0; y = 0; z = 0]
∴ a 1 = 0 ⇒ a = 1
b + 1 = 0 ⇒ b = 1
c + 1 = 0 ⇒ c = 1
∴ 2a 3b + 4c = 2 + 3 4 = 1
Correct Answer: 7 26
Explanation:
Correct Answer: 19 2
Explanation:
Correct Answer: 2
Explanation:
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