Question

find the value

if a+b =8, ab = 15 and a² +b² equal 34,
then find the value of a³ +b³​

Answer 1

$\large\bf\underline{Given:-}$

• a + b = 8
• ab = 15
• a² + b² = 34

$\large\bf\underline {To \: find:-}$

• Value of a³ + b³

$\huge\bf\underline{Solution:-}$

we know that,

»★ a³ + b³ = (a + b)(a² + b² - ab)

putting values of :-

• a + b = 8
• ab = 15
• a² + b² = 34

≫ a³ + b³ = (a + b)(a² + b² - ab)

»» a³ + b³ = (8)(34 - 15)

»» a³ + b³ = 8 × 19

»» a³ + b³ = 152

So, Value of a³ + b³ = 152

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✝️Some identities important :-

(a + b) ² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

a³ + b³ = (a + b)(a² + b² - ab)

a³ - b³ = (a - b)(a² + b² + ab)

a² - b² = (a + b)(a - b)

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \purple{Question:-}}}}}}$

Find the Value : -

If a+b = 8, ab = 15 and a² + b² equal 34 , then find the value of a³ +b³ ..

_______________

${ \huge{ \bold{ \underline{ \underline{ \green{Answer:-}}}}}}$

✒Given :

• a + b = 8
• ab = 15
• a² + b² = 34

✒To Find :

• Value of a³ and b³ ..

✒Identity Used :

• a³ + b³ = (a+b) (a² + b² - ab)

✒On Calculating :

$\dashrightarrow\sf{{a}^{3}+{b}^{3}=(a+b) {(a}^{2}+{b}^{2})}$

$\dashrightarrow\sf{{a}^{3}+{b}^{3}=(8) (34-15)}$

$\dashrightarrow\sf{{a}^{3}+{b}^{3}=8\times{19}}$

$\dashrightarrow\sf{{a}^{3}+{b}^{3}=152}$

✒So, the value of a³ + b³ = 152 ..