SOLUTION: If {{{ (a-b)^2= 289 }}} and {{{ (a+b)^2= 169 }}}, then what is the value of |4ab| ?

Algebra ->  Absolute-value -> SOLUTION: If {{{ (a-b)^2= 289 }}} and {{{ (a+b)^2= 169 }}}, then what is the value of |4ab| ?      Log On


   

Question 1076094: If +%28a-b%29%5E2=+289+ and +%28a%2Bb%29%5E2=+169+, then what is the value of |4ab| ?
Found 3 solutions by ikleyn, MathLover1, MathTherapy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
%28a-b%29%5E2%29 = 289 = a%5E2+-+2ab+%2B+b%5E2,     (1)

%28a%2Bb%29%5E2%29 = 169 = a%5E2+%2B+2ab+%2B+b%5E2.     (2)


Now subtract (1) from (2. You will get

4ab = 169-289 = -120.


Hence, |4ab| = 120.

Answer. |4ab| = 120.

Solved.


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+%28a-b%29%5E2=+289+ and
+%28a%2Bb%29%5E2=+169+
first find a and b
+%28a-b%29%5E2=+289+
+%28a-b%29=+sqrt%28289%29+
+%28a-b%29=+17+ or +%28a-b%29=+-17+
if +%28a-b%29=+17+=>+a=+17%2Bb+
if +%28a-b%29=+-17+=>+a=+-17%2Bb+
from
+%28a%2Bb%29%5E2=+169+ we have
+a%2Bb=+sqrt%28169%29+
+a%2Bb=+13+ or +a%2Bb=+-13+
if +a%2Bb=+13+=> +a=+13-b+
if +a%2Bb=+-13+=> +a=+-13-b+
from +a=+17%2Bb+ and +a=+13-b+ find b
+17%2Bb+=13-b
+b%2Bb+=13-17
+2b+=-4
+b+=-2 ....find a
+a=+17%2B%28-2%29+
+a=+15+
so, one pair of solutions are: +a=+15+ and +b+=-2
from +a=+-17%2Bb+ and +a=+-13-b+ find b
+-17%2Bb+=-13-b
+b%2Bb+=13%2B17
+2b+=+30
+b+=+15 ....find a
+a=+-17%2B15
+a=+-2+
the other pair of solutions are: +a=+-2+ and +b+=15
then what is the value of abs%284ab%29 ?
abs%284ab%29 when +a=+15+ and +b+=-2
abs%284%2A15%2A%28-2%29%29
abs%28-120%29=highlight%28120%29
and
abs%284ab%29 when +a=+-2+ and +b+=15
abs%284%2A%28-2%29%2A15%29
abs%28-120%29=highlight%28120%29



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
If +%28a-b%29%5E2=+289+ and +%28a%2Bb%29%5E2=+169+, then what is the value of |4ab| ?
%28a+-+b%29%5E2+=+289______a%5E2+-+2ab+%2B+b%5E2+=+289 ------- eq (i)

%28a+%2B+b%29%5E2+=+169______a%5E2+%2B+2ab+%2B+b%5E2+=+169 ------- eq (ii) 

4ab = - 120 -------- Subtracting eq (i) from eq (ii)



That’s all. No need to do all types of calculations to get to the answer.

Certainly no need to find a, then b, then 4ab. That's not necessary, at all!