Question

If ( a+b)=6 and 2ab=17.5,find the value of 2a square + 2b square

Answer 1

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Answer 2

Answer:

Required value of $2 {a}^{2} + 2 {b}^{2}$ is 37

Step-by-step explanation:

Given,

$(a + b) = 6$ and $2ab = 17.5$

Now,

$2 {a}^{2} + 2 {b}^{2} \\ = 2 ({a}^{2} + {b}^{2} ) \\ = 2 [{(a + b)}^{2} - 2ab] \\ = 2 ({6}^{2} - 17.5) \\ = 2 \times (36 - 17.5) \\ = 2 \times ( 18.5) \\ = 37$

Here applied formulas are

${a}^{2} + {b}^{2} \\ = {(a + b)}^{2} - 2ab$

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549