Question

if 2x+6y=60 and xy=1, find x^2+9y^2

Answer 1

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$\underline{SOLUTION}$ ➡

$\underline{Given :}\: \\ \\ 2x + 6y = 60 \\ \\ xy = 1 \\ \\ \\ \underline{To \: \: find \: :} \: \: x {}^{2} + 9y {}^{2}$

$Now, \\ \\ 2x + 6y = 60 \\ \\ = > 2(x + 3y) = 60 \\ \\ = > x + 3y = \frac{60}{2} \\ \\ = > x + 3y = 30 \: - - - - > (1)$

$Squaring \: \: both \: \: sides \: \: of \: (1) \: \: we \: \: get,$

$(x + 3y) {}^{2} = (30) {}^{2} \\ \\ = > x {}^{2} + 2 \times x \times 3y + 9y {}^{2} = 900 \\ \\ = > x {}^{2} + 9y {}^{2} + 6xy = 900 \\ \\ = > x {}^{2} + 9y {}^{2} + 6 \times 1 = 900 \: \: \: \: (as \: \: xy \: = 1 \: \: given)\\ \\ = > x {}^{2} + 9y {}^{2} + 6 = 900 \\ \\ = > x {}^{2} + 9y {}^{2} = 900 - 6 \\ \\ = > x {}^{2} + 9y {}^{2} = 894$

$\underline{ANSWER}$ ➡

$\boxed{x {}^{2} + 9y {}^{2} = 894}$

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Answer 2

Answer:

x²+9y²=894

Step-by-step explanation:

Concept

First we have to dividing both sides by 2

and next step we have to do squaring on both sides to the equation of the value

next step  it is in the form of (a+b)2=a2+b2+2ab) so we have to seperate the value and then we get the answer

Given

2x+6y=60

xy=1

To find

We have to find the valu of x²+9y²=?

Given

2x+6y=60

xy=1

To find

We have to find the valu of x²+9y²=?

Solution

2x+6y=60

x+3y=30

(dividing both sides by 2)

(x+3y)²=302

(squaring both sides)

x²+9y²+6yx=900

[ (a+b)2=a2+b2+2ab) constitute that here ]

x²+9y²=900-6*1(x*y=1)

x²+9y²=894

Then the final answer of x²+9y²=894

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