Solve the quadratic equation by factorization method

Ques1. A TAKES 6 DAYS LESS THAN B TO FINISH A PIECE OF WORK IF BOTH A & B TOGETHER CAN FINISH IT IN 4 DAYS ,FIND THE TIME TAKEN BY B TO FINISH THE WORK.FIND ITS SOLUTION ONLY IN quadratic equation form by factorization method
Ques2. TWO CIRCLES TOUCH EXTERNALLY.THE SUM OF THEIR AREA IS 130π SQUARE CM & DISTANCE BETWEEN THEIR CENTRES IS 14 cm .FIND THE RADII OF THE CIRCLES ?FIND ITS SOLUTION ONLY IN quadratic equation form by factorization method

1/a + 1/b = 1/4
1/(b - 6) + 1/b = 1/4
4b + 4b - 24 = b^2 - 6b
b^2 - 14b + 24 = 0
(b - 2)(b + 12) = 0
b = 2 , 12 => reject b = 2 , (less than 6)
b = 12 days

2) let the radii be R and r:
R + r = 14 cm => r = 14 - R
A + a = 130π cm^2
πR^2 + πr^2 = 130π
R^2 + (14 - R)^2 = 130
R^2 + (196 - 28R + R^2) = 130
2R^2 - 28R + 196 - 130 = 0
R^2 - 14R + 33 = 0
(R - 3)(R - 11) = 0
R = 3 , 11 cm
r = 11 , 3 cm

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1) Let B alone take X days to finish a piece of work.

A alone will take (X - 6) days to finish the same piece of work.

In 1 day B alone will finish 1 / X of the work and A alone in 1 day will finish 1 / ( X - 6) of the work.

Since together they finish the work in 4 days , together in 1 day they will finish 1/4 of the work

i.e. 1 / X + 1 / ( X -6) = 1/4

MULTIPLY BOTH SIDES BY X (X-6)*4

4( X -6) + 4X = X ( X -6)

4X -24 + 4X = X^2 -6X

X^2 -14X + 24 = 0

( X -12) ( X - 2) = 0

X = 12 Or 2

X cannot be 2

ANSWER B takes 12 days and A takes 6 days
CHECK
1/12 + 1/6 = ( 1 +2) /12 = 3/12 = 1/4

2) Let the radius of first circle be X cm

Radius of the second circle will be (14 - X ) cm


Sum of the Area of the circles = pi X^2 + pi ( 14 - X)^2