Question

:) If a-b= 7, ab = 5 find a² + b2​

Answer 1

Answer:

59

Step-by-step explanation:

Given :

• a - b = 7
• ab = 5

To Find : a² + b²

Solution :

• Identity : (a - b)² = a² + b² - 2ab

Putting known values.

→ (7)² = a² + b² - 2(5)

→ 49 = a² + b² - 10

→ a² + b² = 49 + 10

→ a² + b² = 59

Hence, the value of a² + b² is 59.

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Other identities which are frequently used :

• (a + b)² = a² + b² + 2ab

• (a + b)(a - b) = a² - b²

• (x + a)(x + b) = x² + (a + b)x + ab

• (a + b)² - (a - b)² = 4ab

Answer 2

$\huge {\tt {Solution :}}$

Given :

• a-b=7
• ab=5

To Find :

• $\sf {a^2+b^2}$

By putting the given value :

$\sf{ : \implies { {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab}} \\ \\ \sf{ : \implies {7^2= {a}^{2} + b^2 -2 \times 5}} \\ \\ \sf{ : \implies {49= a^2 + b^2 - 10}} \\ \\ \sf{ : \implies {49 + 10= a^2 + b^2 }} \\ \\ \sf{ : \implies {59 = a^2 + b^2 }} \\ \\ \sf{ : \implies { a^2 + b^2 = 59 }}$

$\bf {\therefore{The\:value\:of\:a^2 + b^2\: is\: 59.}}$

$\rule {307}{2}$