Question

Kindly answer this question I will give 5 star rating and thanks and mark ur answer brainliest if u will give a proper and good answer

Answer 1

AnsWer :

( c ) 13. ✓

QuestioN :

11. If ab = 6 and a + b = 5 then the value of ( a² + b² ) is

• ( a ) 11.
• ( b ) 12.
• ( c ) 13.
• ( d ) 14.

To FinD :

The value of a² + b² is.

SolutioN :

$\tt \dagger \: \: \: \: \: a + b = 5.$

$\tt: \implies a + b = 5.$

Squaring both Sides.

$\tt: \implies {(a + b )}^{2} = {5 }^{2}$

We know,

• ( a + b )² = a² + b² + 2ab.

$\tt: \implies {a}^{2} + {b}^{2} + 2ab = 25.$

$\tt: \implies {a}^{2} + {b}^{2} + 2(6) = 25.$

$\tt: \implies {a}^{2} + {b}^{2} + 12 = 25.$

$\tt: \implies {a}^{2} + {b}^{2} = 25 - 12.$

$\tt: \implies {a}^{2} + {b}^{2} = 13.$

Therefore, the required answer is 13 Options ( c )

$\rule{200}2$

MorE InformatioN :

• ( a + b )( a - b ) = a² - b².
• ( a + b )² = a² + b² + 2ab.

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer is Option C

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ ab = 6

✭ a+b = 5

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ The Value of (a²+b²)?

$\rule{110}1$

$\huge\sf\purple{Steps}$

Given that a+b = 5, on Squaring both sides,

≫ a²+b² = 5²

≫ a²+b² = 25

We know that,

$\underline{\boxed{\sf (a+b)^2 = a^2+2ab+b^2}}$

On Substituting the given values,

➝ $\sf a^2+2ab+b^2 = 25$

➝ $\sf a^2+b^2+2(6) = 25$

➝ $\sf a^2+b^2+12 = 25$

➝ $\sf a^2+b^2 = 25-12$

➝ $\sf \orange{a^2+b^2 = 13}$

$\rule{130}{1.5}$

$\sf\bullet\:\red{More \ Formulas}$

»» (a-b)² = a²+b²-2ab

»» (a+b)(a-b) = a²-b²

»» (a+b)³ = a³+b³+3ab(a+b)

»» (a-b)³ = a³-b³-3ab(a-b)

»» a³+b³ = (a+b)(a²+b²-ab)

»» a³-b³ = (a-b)(a²+b²+ab)

»» (a+b)² = (a-b)²+4ab

»» (a-b)² = (a+b)²-4ab

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