Question

please please please solve fst u r brilliant I know​

Answer 1

I hope It will help you..

Answer 2

Question: If (a - b) = 7 and a³ - b³ = 133, find (i) ab (ii) a² + b²

Answer:

$\large{\underline{\boxed{\sf ab =-10}}}$

$\large{\underline{\boxed{\sf {a}^{2} + {b}^{2} = 29}}}$

Step-by-step explanation:

$\implies \tt (a - b) = 7 \\ \\ \bf on \: cubing \: both \: sides : \\ \\ \implies \tt (a - b) {}^{3} = (7) {}^{3} \\ \\ \implies \tt a{}^{3} - b {}^{3} - 3ab(a - b) = 343 \\ \\ \implies \tt a{}^{3} - b {}^{3} - 3ab(7) = 343 \\ \\ \implies \tt 133 - 21ab = 343 \\ \\ \implies \tt - 21ab = 343 - 133 \\ \\ \implies \tt - 21ab = 210 \\ \\ \implies \tt ab = - \frac{210}{21} \\ \\ \boxed{ \bf \therefore \: ab = - 10}$

Again,

$\implies \tt (a - b) = 7 \\ \\ \bf Squaring \: both \: sides : \\ \\ \implies \tt (a - b) {}^{2} = (7) {}^{2} \\ \\ \implies \tt {a}^{2} + {b}^{2} - 2ab = 49 \\ \\ \implies \tt {a}^{2} + {b}^{2} - 2( - 10) = 49 \\ \\ \implies \tt {a}^{2} + {b}^{2} + 20 = 49 \\ \\ \implies \tt {a}^{2} + {b}^{2} =49 - 20 \\ \\ \boxed{\bf \therefore \: {a}^{2} + {b}^{2} = 29}$

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★ Identity Used:

• (a - b)³ = a³ - b³ - 3ab(a - b)
• (a - b)² = a² + b² - 2ab