RATIONALIZE THE DENOMINATOR AND FIND THE VALUE OF A AND B
Problem 1 :
Solution:
=3-13+1×3-13-1=3-1232-(1)2=32+(1)2-23(1)3-1=3+1-232=4-232=22-32=2-3=a+b3a=2 and b=-1
Hence, the value of a and b is 2 and -1.
Problem 2 :
Find the value of a and b in 5+237+43=a+b3.
Solution:
=5+237+43×7-437-43=35-203+143-832(7)2-432=35-63-8×349-16×3=35-24-6349-48=11-631=11-63=a+b3a=11 and b=-6
Hence, the value of a and b is 11 and -6.
Problem 3 :
Find the value of a and b in 5-65+6=a-b6.
Solution:
=5-65+6×5-65-6=5-62(5)2-62=(5)2+(6)2-2(5)×625-6=25+6-10619=31-10619=3119-10619=a-b6a=3119 and b=1019
Hence, the value of a and b is 31/19 and 10/19.
Find the value of a and b in each of the following:
Problem 4 :
3+23-2=a+b2
Solution:
=3+23-2×3+23+2=3+22(3)2-22=(3)2+(2)2+2(3)×29-2=9+2+627=11+627=117+627=a+b2a=117 and b=67
Hence, the value of a and b is 11/7 and 6/7.
Problem 5 :
3+73-7=a+b7
Solution:
=3+73-7×3+73+7=3+72(3)2-72=(3)2+(7)2+2(3)×79-7=9+7+672=16+672=28+372=8+37=a+b7a=8 and b=3
Hence, the value of a and b is 8 and 3.
Problem 6 :
7+57-5=a+b5
Solution:
=7+57-5×7+57+5=7+52(7)2-52=(7)2+(5)2+2(7)×549-5=49+5+14544=54+14544=227+7544=27+7522=2722+7522=a+b5a=2722 and b=722
Hence, the value of a and b is 27/22 and 7/22.