Question

Given that 2m + 5n = 9 and mn = 1, find the value of 4m^2 + 25n^2​

Answer 1

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Answer 2

Answer:

The value of 4m² + 25n² is 61.

Step-by-step-explanation:

We have given that,

2m + 5n = 9 and

mn = 1

We have to find the value of 4m² + 25n².

Now,

4m² + 25n² = ( 2m )² + ( 5n )²

Now, we know that,

a² + b² = ( a + b )² - 2ab

∴ ( 2m )² + ( 5n )² = ( 2m + 5n )² - 2 * ( 2m ) * ( 5n )

⇒ 4m² + 25n² = ( 9 )² - 2 * 2 * 5 * mn

⇒ 4m² + 25n² = 81 - 20 * 1

⇒ 4m² + 25n² = 81 - 20

⇒ 4m² + 25n² = 61

∴ The value of 4m² + 25n² is 61.

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Additional Information:

Some algebraic identities:

1. ( a + b )² = a² + 2ab + b²

2. ( a - b )² = a² - 2ab + b²

3. ( a + b )³ = a³ + 3a²b + 3ab² + b³

4. ( a - b )³ = a³ - 3a²b + 3ab² - b³

5. a² + b² = ( a + b )² - 2ab

6. a² - b² = ( a + b ) ( a - b )

7. a³ + b³ = ( a + b ) ( a² + b² - ab )

8. a³ - b³ = ( a - b ) ( a² + b² + ab )

9. ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ac