Question

if a+b=5 and ab =7 then find a²+b²​

Answer 1

$\huge \fcolorbox{red}{yellow}{ \bf \blue{11}}$

Step-by-step explanation:

QUESTION :-

If “a + b = 5”and “ab = 7”, then find “a² + b²”

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SOLUTION :-

GIVEN -

• a + b = 5
• ab = 7

$\:$

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METHOD 1 :-

[note :- (a + b)² = a² + b² + 2ab]

$\bf a + b = 5$

[by squaring both sides]

$\bf{(a + b)}^{2} = {5}^{2}$

$\bf = > {a}^{2} + {b}^{2} + 2ab = 25$

[put the value of 'ab' ]

$\bf = > {a}^{2} + {b}^{2} + 2(7) = 25 \\ \\ \bf = > {a}^{2} + {b}^{2} + 14 = 25 \\ \\ \bf = > {a}^{2} + {b}^{2} = 25 - 14 \\ \\ \bf = > \underline \color{green}{ {a}^{2} + {b}^{2} = 11}$

Hence,

The value of a² + b² is 11 .

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METHOD 2 :-

[note :- a² + b² = (a + b)² - 2ab]

So,

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

[put the values of 'a+b' and 'ab']

$\bf = {(5)}^{2} - 2(7) \\ \\ = \bf25 - 14 \\ \\ \bf =11$

$\bf = > \underline \color{brown}{ {a}^{2} + {b}^{2} = 11}$

Hence,

The value of a² + b² is 11 .

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MORE TO KNOW :-

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

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Hope it helps.

#BeBrainly :-)

Answer 2

Answer:

$\rm \qquad \pink{a^2+b^2=11}$

Step-by-step explanation:

$\sf \red{ We \: have,}$

$\rm \qquad \blue{ a+b=5}$

$\rm \qquad \blue{ab=7}$

$\sf \red{To \: find,}$

$\rm \qquad \blue{a^2 +b^2 =?}$

$\sf \red{Solution:-}$

$\rm \qquad \: \green{ a+b=5}$

$\rm \qquad \green{(a+b)^2 =25}$

$\rm \qquad \green{a^2+b^2+2ab=25}$

$\rm \qquad \green{a^2+b^2+2×7=25}$

$\rm \qquad \green{a^2+b^2=25-14}$

$\rm \qquad \pink{a^2+b^2=11}$