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If 3x + 4y = 16 and xy = 4, find the value of 9x2 + 16y2. - Mathematics

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प्रश्न

If 3x + 4y = 16 and xy = 4, find the value of 9x2 + 16y2.

योग
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उत्तर

Given that (3x + 4y) = 16 and xy = 4,

We need to find 9x2 + 16y2,

We know that,

(a + b)2 = a2 + b2 + 2ab

Consider the square of 3x + 4y:

∴ (3x + 4y)2 = (3x)2 + (4y)2 + 2 × 3x × 4y

⇒ (3x + 4y)2 = 9x2 + 16y2 + 24xy     ...(1)

Substitute the values of (3x + 4y) and xy,

In the above equation (1), we have,

(3x + 4y)2 = 9x2 + 16y2 + 24xy

⇒ (16)2 = 9x2 + 16y2 + 24(4)

⇒ 256 = 9x2 + 16y2 + 96

⇒ 9x2 + 16y2 = 256 − 96

∴ 9x2 + 16y2 = 160

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Expansions (Including Substitution) - Exercise 4 (A) [पृष्ठ ५८]

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सेलिना Concise Mathematics [English] Class 9 ICSE
अध्याय 4 Expansions (Including Substitution)
Exercise 4 (A) | Q 14 | पृष्ठ ५८
बी निर्मला शास्त्री Mathematics [English] Class 9 ICSE
अध्याय 3 Expansions
EXERCISE A | Q 12. | पृष्ठ ३२
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