Question

2x+3y=13 and xy=6 then 4x^2+9y^2 = ?

Answer 1

Answer:

(2x + 3y)³ = 2197

Using (a + b)³ = a³ + b³ + 3 ab (a + b) ,

= > 8x³ + 27y³ + 3 × 2 x × 3 y (2 x + 3 y ) = 2197

= > 8x³ + 27y³ + 18 xy(13) = 2197

= > 8x³ + 27y³ + 18×6×13 = 2197

= > 8x³ + 27y³ + 1404 = 2197

= > 8x³ + 27y³ = 2197 - 1404

= > 8x³ + 27y³ = 793

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Answer 2

EXPLANATION.

⇒ 2x + 3y = 13. - - - - - (1).

⇒ xy = 6. - - - - - (2).

As we know that,

Formula of :

⇒ (a + b)² = a² + b² + 2ab.

Using this formula in this question, we get.

Squaring on both sides of the equation (1), we get.

⇒ (2x + 3y)² = (13)².

⇒ (2x)² + (3y)² + 2(2x)(3y) = 169.

⇒ 4x² + 9y² + 12xy = 169.

Put the value of equation (2) in this expression, we get.

⇒ 4x² + 9y² + 12(6) = 169.

⇒ 4x² + 9y² + 72 = 169.

⇒ 4x² + 9y² = 169 - 72.

⇒ 4x² + 9y² = 97.

∴ The value of 4x² + 9y² is 97.