Question

IF A+B=5 and A-B = 3
then 2A²+2B²=?

​

Answer 1

Answer:

34

Step-by-step explanation:

A=4 ,B=1

2(16)+2(1)

32+2

34

Answer 2

$\large \sf\underline{ \underline{ \red{given : }}} \:$

• A + B = 5

• A - B = 3

$\\ \\ \large \sf\underline{ \underline{ \red{to \: find: }}}$

• 2A² + 2B²

$\\ \\ \large \sf\underline{ \underline{ \red{to \: know : }}} \\ \\ \\ \boxed{ \pink{ ( {x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}} } \\ \\ \\ \boxed{ \pink{( {x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }}$

$\\ \large \sf\underline{ \underline{ \red{solution : }}}$

We know ,

➤ A + B = 5

Squaring both sides we get ,

➟ ( A + B )² = 5²

➟ A² + 2AB + B² = 25

➟ A² + B² = 25 - 2AB ㅤㅤㅤㅤ----( 1 )

▬▬▬▬▬▬▬▬▬▬

➤ A - B = 3

Squaring both sides we get ,

➟ ( A - B )² = 3²

➟ A² - 2AB + B² = 9

➟ A² + B² = 9 + 2ABㅤㅤㅤㅤ----( 2 )

▬▬▬▬▬▬▬▬▬▬

➨ Adding equation (1) and (2) ,

A² + B² + A² + B² = 25 - 2AB + 9 + 2AB

➾ 2A² + 2B² = 34