Math, asked by soham200839, 1 year ago

2. If (a - b) = 5 and ab = 14 ; find the value of a^2 + b^2.

Answers

Answered by kaushaltanisha730
0

Step-by-step explanation:

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Answered by arunyadav1973
0

Step-by-step explanation:

(a-b) =5

a-b =5

a=5+b....1

ab = 14.....2

Using equation 1 in equation 2

ab = 14

(5+b) b = 14

 {b}^{2}  + 5b = 14 \\  {b}^{2}  + 5b - 14 = 0 \\ by \: fractoristion \: method \\  {b}^{2} + 7b - 2b - 14 = 0 \\ ( {b}^{2}   + 7b)( - 2b - 14) = 0 \\ b(b + 7) - 2(b + 7) = 0 \\( b   + 7)(b - 2) = 0 \\ ( b   + 7) = 0 \:  \: or \:  \: (b - 2) = 0 \\ b = -  7 \:  \: or \:  \: b = 2

From equation 1

a=5+b

a = 5 + (-7) or a = 5+2

a = -2. or a= 7

 for \: a =  - 2 \:  \:  \:  \:  \: b \:  =  - 7 \\  {a}^{2}  +  {b}^{2}  =  {( - 2})^{2}  +  {( - 7})^{2}  \\  = 4 + 49 = 53

for \: a = 7 \:  \:  \:  \:  \:  \:  \:  \: b = 2 \\  {a}^{2}  +  {b}^{2}  =  {7}^{2}  +  {2}^{2}  = 49 + 4 = 53

for \: a = 7 \:  \:  \:  \:  \:  \:  \:  \:  \:  \: b =  - 7 \\  {a}^{2}  +  {b}^{2}  =  {7}^{2}  +  {( - 7)}^{2} = 49 + 49 = 98

for \: a =  - 2 \:  \:  \:  \:  \:  \:  \:  \:  \: b = 2 \\  {a}^{2}  +  {b}^{2}  =  { - 2}^{2} +  {2}^{2}   = 4 + 4 = 8

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