Question

if a+b+c=10 and a^2+ b^2+c^2=48, find the value of ab+bc+ac​

Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

• If a + b + c = 10 and a² + b² + c² = 48, Find the value of ab + bc + ac

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♣ ᴀɴꜱᴡᴇʀ :

• ab + bc + ac  = 26

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♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

We all are aware of :

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

We have :

a + b + c = 10

a² + b² + c² = 48

Substituting the values :

(10)² = a² + b² + c² + 2ab  + 2bc  +  2ac

100 = 48 + 2ab  + 2bc  +  2ac

Solve for 2ab  + 2bc  +  2a

Subtracting 48 from both sides :

100 - 48 = 48 + 2ab  + 2bc  +  2ac  - 48

52 = 2ab  + 2bc  +  2ac

52 =  2(ab + bc + ac)

Dividing both sides by 2 :

52/2 =  [2(ab + bc + ac)]/2

26  = ab + bc + ac

Switch sides :

ab + bc + ac  = 26

Answer 2

Answer:

$\underline{ \sf{ \underline{ \sf{☃Given:}}}}$

• a + b + c = 10
• a² + b² + c² = 48

$\underline{ \sf{ \underline{☃Find: }}}$

• ab + bc + ac

$\underline{ \sf{ \underline{☃Solution:}}}$

From the formula ⤵

${ \boxed{ \sf{(a+b+c) ² = a²+b²+c²+2ab+2bc+2ca}}}$

From question we have that

• a + b + c = 10
• a² + b² + c² = 48

Substitute the following values in the formula:-

${ \to{ \sf{ {(10)}^{2} = 48 + 2ab + 2bc + 2ca}}}$

${ \to{ \sf{100 = 48 + 2ab + 2bc + 2ca}}}$

${ \to{ \sf{100 - 48 = 2ab + 2bc + 2ca}}}$

${ \to{ \sf{52 = 2ab + 2bc + 2ca}}}$

${ \to{ \sf{52 = 2(ab + bc + ca)}}}$

${ \to{ \sf{ \frac{52}{2} = ab + bc + ca}}}$

${ \to{ \sf{26 = ab + bc + ca}}}$

${ \therefore{ \sf{Value \: of \: ab+bc+ca = 26}}}$