Question

Find the values of the following expressions: 36x²+49y²+84 xy, when x = 1/4, y = 2/7 proper solution​

Answer 1

Answer:

answer for the given problem is given

Answer 2

Given

x = 1/4 and y = 2/7

To Find

Value of 36x^2 + 49y^2 + 84xy

Answer and explanation

We know the identity

${x}^{2} + {y}^{2} + 2xy = {(x + y)}^{2}$

See here

$36 {x}^{2} + 49 {y}^{2} + 84xy$

Wee see

36x^2 = ( 6x )^2

49y^2 = ( 7y )^2

84xy = 2 × 6x × 7y

The expression becomes

$({6x})^{2} + ( {7y})^{2} + 2 \times 6x \times 7y$

So the expression simplifies further to

${(6x + 7y)}^{2}$

According to our identity

Now given

x = 1/4 and y = 2/7

Put it in our simplifies expression

${(6 \times \frac{1}{4} + 7 \times \frac{2}{7}) }^{2}$

${( \frac{3}{2} + 2)}^{2}$

${ (\frac{7}{2}) }^{2}$

$\frac{49}{4}$

This the required answer

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