Question

find the value of 4 x square + 9 y square if 2 X + 3 y = 18 and xy = 5​

Answer 1

Step-by-step explanation:

$\bf{\huge\mathcal{\boxed{\rm{\mathfrak\blue{Hey Mate:}}}}}$

Given :

2x + 3y = 18 & xy = 5

• (2x + 3y)² = 4x² + 9y² + 2(2x)(3y)
• Or, (18)² = 4x² + 9y² + 2(2x)(3y)
• 4x² + 9y² = 324 - 12xy
• 4x² + 9y² = 324 - 12*5
• 4x² + 9y² = 264

Answer 2

$\huge\bigstar\underline\mathfrak\red{Answer}$

$\huge\boxed{4x\:square\:+\:9y\:square\:=\:264}$

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$\huge\bigstar\underline\mathfrak\red{Explanation}$

Given : 2x + 3y = 18 and xy = 5

To find : The value of 4x² + 9y²

Solution : We know that,

(a+b)² = a² + b² + 2ab

Let, 2x be a and 3y be b.

Now, put a = 2x and b = 3y in the above identity.

(2x+3y)² = (2x)² + (3y)² + 2(2x)(3y) .....(i).

Now, put the given values in eq (i)

(18)² = 4x² + 9y² + 12(5)

324 = 4x² + 9y² + 60

324 - 60 = 4x² + 9y²

4x² + 9y² = 264 ( required answer )