Question

if a+b=19 and ab =88 find a-b given{a>b​

Answer 1

Answer :

a - b = +3

Step-by-step explanation :

Given,

• a + b = 19
• ab = 88

To find,

• a - b = ?

Solution,

 we know,

 (a + b)² = a² + b² + 2ab

Substituting the values of (a + b) and ab,

➙  (19)² = a² + b² + 2(88)

➙  361 = a² + b² + 176

➙  a² + b² = 361 - 176

➙  a² + b² = 185

we also know,

  (a - b)² = a² + b² - 2ab

Substituting the values of (a² + b²) and ab,

➙ (a - b)² = 185 - 2(88)

➙ (a - b)² = 185 - 176

➙ (a - b)² = 9

➙ (a - b) = √9

➙ (a - b) = ±3

➙ a - b = +3 , -3

Since, a > b ; a - b will be positive.

➙ a - b = 3

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Algebraic identities :

 $\boxed{\begin{minipage}{6 cm} 1)\sf\:(A+B)^{2} = \sf A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\sf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\sf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\sf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{minipage}}$