If x2 + 4y2 = 4xy, then x : y is : 1. 1 : 1 2. 1 : 2 3. 1 : 4 4. 2 : 1

Given, x2 + 4y2 = 4xy Dividing the equation by y2, Let . Then ⇒ k2 + 4 = 4k ⇒ k2 - 4k + 4 = 0 ⇒ k2 - 2k - 2k + 4 = 0 ⇒ k(k - 2) - 2(k - 2) = 0 ⇒ (k - 2)(k - 2) = 0 ⇒ (k - 2)= 0 [Using Zero-product rule] ⇒ k = 2 Therefore, Hence, option 4 is the correct option.

Mathematics

If x² + 4y² = 4xy, then x : y is :
1 : 1
1 : 2
1 : 4
2 : 1

Ratio Proportion

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Answer

Given,

x² + 4y² = 4xy

Dividing the equation by y²,

$\therefore \Big(\dfrac{x}{y}\Big)^2 + 4 = 4\Big(\dfrac{x}{y}\Big)$

Let $\dfrac{x}{y} = k$ . Then

⇒ k² + 4 = 4k

⇒ k² - 4k + 4 = 0

⇒ k² - 2k - 2k + 4 = 0

⇒ k(k - 2) - 2(k - 2) = 0

⇒ (k - 2)(k - 2) = 0

⇒ (k - 2)= 0 [Using Zero-product rule]

⇒ k = 2

Therefore, $\dfrac{x}{y} = k = \dfrac{2}{1}$

Hence, option 4 is the correct option.

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Mathematics

If x² + 4y² = 4xy, then x : y is :
1 : 1
1 : 2
1 : 4
2 : 1

Ratio Proportion

Answer

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Mathematics

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Ratio Proportion

Answer

Related Questions

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If x² + 4y² = 4xy, then x : y is :
1 : 1
1 : 2
1 : 4
2 : 1

Of 132 examinees of a certain class, the ratio of passed to failed students is 9 : 2. If 4 more students passed, what would have been the ratio of passed to failed students?
3 : 28
28 : 5
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2 marbles from P to Q and 1 from R to Q
3 marbles from Q to R
4 marbles from R to Q
5 marbles from R to P

If 3A = 5B and 4B = 6C, then A : C is equal to :
2 : 5
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If, A : B = 7 : 9 and B : C = 5 : 4, then A : B : C is:
7 : 45 : 36
28 : 36 : 35
35 : 45 : 36
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