Question

3. If a + b = 10 and ab = 16, find the value of a² - ab + b²​

Answer 1

${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} \\ {10}^{2} = {a}^{2} + {b}^{2} + 2 \times 16 \\ 100 = {a}^{2} + {b}^{2} \times 16 \\ {a}^{2} + {b}^{2} = \frac{100}{16 } \\ \\ {a}^{2} + {b}^{2} = \frac{25}{9}$

So,

${a}^{2} - ab + {b}^{2} \\ = {a}^{2} + {b}^{2} - ab \\ = \frac{25}{9} - 16 \\ = \frac{25 - 144}{9} = \frac{119}{9}$

hope it will help u ✨☺️

Answer 2

Answer:

⇒a+b=10

⇒ab=16

⇒(a+b) 2=a ^2+b√ 2+2ab

⇒10 ^2 =a ^2 +b ^2 +2(16)

∴a ^2 +b ^2=68

⇒a ^2+b^ 2+ab=68+16=84

⇒a ^2+b ^2−ab=68−16=52

Step-by-step explanation:

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