Quadratic Equation
Direction: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer
( 1 ) x > y
( 2 ) x ≥ y
( 3 ) x < y
( 4 ) x ≤ y
( 5 ) x = y or the relationship cannot be established.
- Ⅰ. x3 × 13 = x2 × 247
Ⅱ. y1/3 × 14 = 294 ÷ y2/3
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As per the given above equations , we have
Ⅰ. x3 × 13 = x2 × 247⇒ x3 = 247 x2 13
Ⅱ. y1/3 × 14 = 294 ÷ y2/3
⇒ y1/3 × y2/3 = 21⇒ y1/3 × y2/3 = 294 14
Correct Option: C
As per the given above equations , we have
Ⅰ. x3 × 13 = x2 × 247⇒ x3 = 247 x2 13
∴ x = 19
Ⅱ. y1/3 × 14 = 294 ÷ y2/3
⇒ y1/3 × y2/3 = 21⇒ y1/3 × y2/3 = 294 14
∴ y = 21
Clearly, x < y is correct answer .
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Ⅰ. 2 × 4 - 3 × 4 = x10/7 x4/7 x4/7
Ⅱ. y3 + 783 = 999
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According to question ,we have
Ⅰ. 12 × 4 - 3 × 4 = x10/7 x4/7 x4/7 ⇒ 48 - 12 = x10/7 x4/7 x4/7 ⇒ 48 - 12 - = x10/7 x4/7
Ⅱ.
y3 + 783 = 999
⇒ y3 = 999 - 783 ⇔ y3 = 216
Correct Option: D
According to question ,we have
Ⅰ. 12 × 4 - 3 × 4 = x10/7 x4/7 x4/7 ⇒ 48 - 12 = x10/7 x4/7 x4/7 ⇒ 48 - 12 - = x10/7 x4/7
⇒ 36 = x(10/7) + (4/7) ⇔ 36 = x2
∴ x = √36 = ± 6
Ⅱ. y3 + 783 = 999
⇒ y3 = 999 - 783 ⇔ y3 = 216
∴ y = ∛216 ≤ 6
Clearly, we can say that required answer is x ≤ y .
- Ⅰ. ( 17 )2 + 144 ÷ 18 = x
Ⅱ. ( 26 )2 - 18 × 21 = y
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According to question , we have
From equation Ⅰ.
( 17 )2 + 144 ÷ 18 = x⇒ x = 172 + 144 × 1 18
From equation Ⅱ.
( 26 )2 - 18 × 21 = y
⇒ y = 262 - 18 × 21
Correct Option: C
According to question , we have
From equation Ⅰ.
( 17 )2 + 144 ÷ 18 = x
∴ x = 289 + 8 = 297⇒ x = 172 + 144 × 1 18
From equation Ⅱ.
( 26 )2 - 18 × 21 = y
⇒ y = 262 - 18 × 21
∴ y = 676 - 378 = 298
From above equations it is clear that correct answer is x < y .
- Ⅰ. x2 – 11x + 24 = 0
Ⅱ. 2y2 – 9y + 9 = 0
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According to question ,we can say that
From equation Ⅰ.
x2 – 11x + 24 = 0
⇒ x2 – 8x – 3x + 24 = 0
From equation Ⅱ.
2y2 – 9y + 9 = 0
⇒ 2y2 – 3y – 6y + 9 = 0Correct Option: B
According to question ,we can say that
From equation Ⅰ. x2 – 11x + 24 = 0
⇒ x2 – 8x – 3x + 24 = 0
⇒ x(x – 8) – 3(x – 8) = 0
⇒ (x – 3)(x – 8) = 0
There4; x = 3 or, 8
From equation Ⅱ. 2y2 – 9y + 9 = 0
⇒ 2y2 – 3y – 6y + 9 = 0
⇒ y(2y – 3) – 3(2y – 3) = 0
⇒ (2y – 3)(y – 3) = 0
∴ x ≥ y∴ y = 3 or, 3 2
From above equations it is clear that x ≥ y is correct answer .
- Ⅰ. √500x + √402 = 0
Ⅱ. √360y + ( 200 )1/2 = 0
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As per the given above equations , we can say that
Ⅰ.
√500x + √402 = 0
⇒ √500x = - √402
Ⅱ.
√360y + ( 200 )1/2 = 0
⇒ √360y = - √200
∴ y = - √( 200 / 360 ) = - 0.74Correct Option: C
As per the given above equations , we can say that
Ⅰ.
√500x + √402 = 0
⇒ √500x = - √402
∴ x = - √( 402/500 ) = - √( 400/500 ) = - 0.9
Ⅱ. √360y + ( 200 )1/2 = 0
⇒ √360y = - √200
∴
y = - √( 200 / 360 ) = - 0.74
Clearly, we can see that x < y is required answer .
